Many Republicans are hoping for financial support from President Trump, whose fund-raising power in the party remains unmatched despite his low poll numbers.

© Meridith Kohut for The New York Times

Letters obtained by Guardian and AP contradict testimony that 2019 visit to Samoa had ‘nothing to do with vaccines’

Newly obtained documents indicate that the US health secretary, Robert F Kennedy Jr, lied during two congressional hearings last year, when he told lawmakers who held the key to his confirmation that a 2019 visit to Samoa had “nothing to do with vaccines”.

Letters obtained by the Guardian and the Associated Press contradict that testimony. In one he wrote to the Samoan prime minister before the trip, Kennedy explicitly said he wanted to study the measles, mumps and rubella (MMR) vaccine in the Pacific island nation. In it, he used the words “vaccine” or “vaccination” eight times.

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© Photograph: Nathan Howard/Reuters

© Photograph: Nathan Howard/Reuters

© Photograph: Nathan Howard/Reuters

Senator Darline Graham has spoken far more about her desire to support President Trump’s agenda than she has talked about her brother’s political goals — or her own.

© Haiyun Jiang/The New York Times

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A US military strike on an alleged drug trafficking boat in the Caribbean on Tuesday killed four people, officials said.

US Southern Command (SOUTHCOM) said in a post on X that the strike targeted a vessel “operating along established narco-trafficking routes in the Caribbean.”

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© Photograph: Brian Snyder/Reuters

© Photograph: Brian Snyder/Reuters

© Photograph: Brian Snyder/Reuters

The former Democratic-turned-independent senator and his daughter are backing independent bids for the House and the Senate to try to weaken the two-party grip on the Capitol.

© Jason Andrew for The New York Times

The incumbent senator Dan S Sullivan has condemned ex-school teacher Dan J Sullivan, claiming he is running at the behest of Democrats to confuse supporters

Dan S Sullivan, the Republican senator, will be joined on the November ballot in Alaska by a challenger with a nearly identical name from the same party, election officials confirmed on Tuesday, adding a twist to what is expected to be one of the most hotly contested races of the midterms.

The Republican senator is running for a third term against Democrat Mary Peltola, a former US House representative whom polls show is neck-and-neck with him in a state that hasn’t sent a Democrat to the Senate since 2008.

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© Composite: Sullivan for Senate, CQ-Roll Call via Getty Images

© Composite: Sullivan for Senate, CQ-Roll Call via Getty Images

© Composite: Sullivan for Senate, CQ-Roll Call via Getty Images

A long-shot candidate with the same name as the incumbent Republican senator will be on the ballot in November. That could be a problem for the G.O.P.

© Christopher Miller for The New York Times

President Trump went all in for Senator Darline Graham in a primary runoff on Tuesday. It worked, preserving his undefeated streak in Republican Senate primaries this year.

© Sean Rayford for The New York Times

Darline Graham, sister of late Lindsey Graham and backed by Trump, overcomes concern about lack of experience

South Carolina voters have chosen Darline Graham as the Republican nominee for US Senate, the seat formerly held by her late brother, Lindsey, on November’s ballot.

Darline Graham, with Donald Trump’s full-throated support, overcame concern about her lack of legislative experience to beat five-term congressman Ralph Norman in Tuesday’s Republican special primary runoff.

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© Photograph: Evan Vucci/Reuters

© Photograph: Evan Vucci/Reuters

© Photograph: Evan Vucci/Reuters

Ms. Graham, who is temporarily filling the seat long held by her late brother, Senator Lindsey Graham, prevailed in a runoff and will be heavily favored in November.

© Sean Rayford for The New York Times

Republicans had hoped that a Supreme Court decision allowing party committees to coordinate with candidates would also entitle them to lower ad rates. On Tuesday, an appeals court said otherwise.

© Kendrick Brinson for The New York Times

Ms. Graham is currently serving out the term of her late brother, Lindsey Graham. She has argued that her lack of political experience is a strength.

© Alex Kent/The New York Times

Mr. Norman, a five-term congressman, is a hard-line conservative running against the sister of the late Senator Lindsey Graham.

© Will Crooks for The New York Times

The results of primary runoff elections will likely be known by late Tuesday night, officials said.

© Sean Rayford for The New York Times

Family dynasties are common in American politics. But sibling succession is rare.

© Haiyun Jiang/The New York Times

Runoffs in the state are typically sleepy, but the Republican Senate contest between Darline Graham and Ralph Norman seemed to be drawing relatively high turnout.

© Sean Rayford for The New York Times

The Republican Senate candidate announced the plan with a graphic flagged as ‘Made with AI’

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Ken Paxton, a Republican candidate for the US Senate in Texas, has unveiled plans to tackle the “negative impact” of datacenters amid a growing backlash across the political spectrum.

Paxton, endorsed by Donald Trump but facing a close contest against Democrat James Talarico, posted a “Texas first” datacenter plan on X with a graphic that the social media network flagged as “Made with AI”.

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© Photograph: Bob Daemmrich/ZUMA Press Wire/Shutterstock

© Photograph: Bob Daemmrich/ZUMA Press Wire/Shutterstock

© Photograph: Bob Daemmrich/ZUMA Press Wire/Shutterstock

Republicans who have mostly refrained from criticizing the president’s actions have been vocal in opposition to the move, which they say will harm their constituents.

© Loren Elliott for The New York Times

Republican nominee to face Democrat Annie Andrews in midterm after rushed campaigns for Lindsey Graham’s seat

Reese Boyd, the chair of the Horry county Republican party marveled on Monday afternoon at how little time Senator Darline Graham and Representative Ralph Norman have had to campaign for the Senate primary: “This is not the normal way of things.”

“This is something that usually lasts at least, you know, the better part of a year,” he said. “People normally spend the better part of 18 months getting ready for it. Who knows? This may be the right way to do it? Who knows.”

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© Photograph: Anadolu/Getty Images

© Photograph: Anadolu/Getty Images

© Photograph: Anadolu/Getty Images

Pennsylvania Republicans now view John Fetterman, the state’s Democratic senator, more favorably than its sitting G.O.P. senator, a New York Times/Philadelphia Inquirer/Siena poll found.

© Edison Wu/The New York Times

President Trump’s endorsement track record is on the line in two races, including the high-profile contest to succeed the late Senator Lindsey Graham.

© Meg Kinnard/Associated Press

In a smiling yet tense interview, Dr. Abdul El-Sayed, the Democratic nominee for Senate in Michigan, argued that his Republican critics were using culture-war issues to distract from Americans’ economic concerns.

© Nick Hagen for The New York Times

The president has made a big bet on a senator’s sister.

© The New York Times, left, Reuters

The president rallied for the sister of Lindsey Graham in her South Carolina Senate run and pressured allies to endorse her. A super PAC run by his advisers has spent nearly $800,000 on her campaign. Will it be enough?

© Alex Kent/The New York Times

The ultraconservative congressman who has broken with the president on spending is hoping voters reward his experience, contrarian streak and all.

© Will Crooks for The New York Times

The Democratic and the Republican candidate each blame the other for the bungled recovery effort after storm struck region

Two years after North Carolina suffered the worst natural disaster in its history when Hurricane Helene struck the state’s western half, life in the hardest-hit areas appears back to normal. Downtowns are lively, blocked roads have been reopened and rivers are flowing below their banks.

But the telltale evidence of the disaster’s expensive impacts can still be seen – from “for rent” signs in storefronts whose businesses never came back to debris from the storm still lurking in some waterways. And in the race for North Carolina’s US Senate seat, it’s almost as if the hurricane never left.

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© Photograph: Mario Tama/Getty Images

© Photograph: Mario Tama/Getty Images

© Photograph: Mario Tama/Getty Images

Endorsement of Republican incumbent over challenger with same name adds twist to unusual campaign in Alaska

• Republican senator Dan Sullivan and Democrat Mary Peltola advance in Alaska Senate primary

Dan Sullivan supports Dan Sullivan against Dan Sullivan in Alaska’s US Senate election, says a former Alaskan mayor who recently backed the race’s Republican incumbent over a challenger sharing their name.

That development provided another of multiple absurd elements to Dan S Sullivan’s campaign for a third term in the US Senate, which – beside Mary Peltola, a former Alaska Democratic congresswoman – has drawn opposition from Dan J Sullivan.

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© Photograph: Mark Thiessen; Becky Bohrer/AP

© Photograph: Mark Thiessen; Becky Bohrer/AP

© Photograph: Mark Thiessen; Becky Bohrer/AP

From South Dakota to Alaska, independents are challenging incumbent Republicans and eschewing a Democratic label that Western voters find toxic.

© Alex Hecht for The New York Times

The pro-Israel group has been preparing to spend big for Mike Rogers, the Republican nominee for Senate in Michigan. Does he want that?

© Paul Sancya/Associated Press

A plan to lower tariffs on imported beef and trade tensions with Canada have compounded some G.O.P. worries about a central issue in the midterms.

© Al Drago for The New York Times

Michigan Senate nominee and others have re-energized one-time Democratic voters who abandoned the party under Biden

Two years ago, Zainab Bibi Ahmed thought she had turned her back on the Democrats for good. Now, she is volunteering for the party’s US Senate nominee in Michigan, Abdul El-Sayed.

Ahmed was one of 100,000 people to vote uncommitted in the February 2024 Democratic Michigan primary, in a bid to send a message to then US president Joe Biden about his support for Israel, as people watched what Amnesty International later called a “live-streamed genocide” in Gaza on their screens.

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© Photograph: Jeff Kowalsky/AFP/Getty Images

© Photograph: Jeff Kowalsky/AFP/Getty Images

© Photograph: Jeff Kowalsky/AFP/Getty Images

With opposition to the centers mounting, many Democrats and a growing number of Republicans are campaigning against them.

© Aubrey Trinnaman for The New York Times

With an unpopular war and high prices agitating voters, members of both parties see parallels to an election cycle when Democrats romped. But a lot has changed.

© Doug Mills/The New York Times

A governor’s race, a Senate contest and enough congressional contests to swing control of the House are all in play in Ohio, where voters of all stripes express a deep sense of powerlessness.

© Madeleine Hordinski for The New York Times

Kassebaum Baker became the first woman elected to the US Senate without following a spouse into office

Nancy Kassebaum Baker, a Kansas governor’s daughter who became the first woman elected to the US Senate without following a spouse into office, has died. She was 94.

Kassebaum Baker died on Friday of natural causes, according to her son, Bill Kassebaum.

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© Photograph: Carolyn Kaster/AP

© Photograph: Carolyn Kaster/AP

© Photograph: Carolyn Kaster/AP

A moderate Republican from Kansas, she served three terms before tiring of political strife. “I couldn’t get elected today,” she said in 2013.

© Stephen Crowley/The New York Times

Angie Nixon, a state lawmaker from Jacksonville, shocked Democrats in red Florida by soundly defeating her centrist primary opponent. Now comes the hard part.

© Saul Martinez for The New York Times

President Trump was in South Carolina to stump for Darline Graham, sister of Lindsey. But his own political future was on his mind, too.

© Alex Kent/The New York Times

The South Carolina senator has argued that her lack of political experience is a strength as she runs to succeed her late brother, Lindsey Graham. But a debate misstep has rattled some of her supporters.

© Sean Rayford/Getty Images

The pen Mr. Paxton pocketed more than a decade ago has resurfaced as a campaign issue.

She made the statement during a debate when asked about potential threats to US national security in South China Sea

• US politics live – latest updates

Asked whether Taiwan and the South China Sea threaten US national security, Republican fill-in senator Darline Graham hesitated. “I’m just going to be honest here,” she told Tuesday night’s debate audience. “I’m – not that informed on national security, so – but I do support the military.”

Gasps, and boos, rolled through the opera house hosting the only debate before next week’s Republican runoff – a race to succeed her brother, Lindsey Graham, who was one of the Senate’s most committed rightwing foreign policy hawks before his sudden passing in July. She did not retreat.

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© Photograph: Anadolu/Getty Images

© Photograph: Anadolu/Getty Images

© Photograph: Anadolu/Getty Images

Result tees up marquee race in US midterm elections, which could decide if Republicans or Democrats control Senate

Incumbent Dan S Sullivan, the US senator, advanced in Alaska’s non-partisan primary race for his seat on Tuesday alongside Mary Peltola, a former Democratic congresswoman.

With the top four candidates moving forward from Alaska’s open primaries to the general election, the Associated Press reported that Sullivan and Peltola had qualified for November’s general election.

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© Composite: Getty

© Composite: Getty

© Composite: Getty

Both parties see Alaska as key to winning the Senate. The state’s nonpartisan primary put Mary Peltola, a Democratic former congresswoman, on the same ballot as Dan Sullivan, the incumbent Republican she hopes to unseat. Both advanced to the general election.

© Kerry Tasker/Reuters; Eric Lee for The New York Times

State Representative Angie Nixon, a progressive firebrand, marshaled grass-roots enthusiasm to defeat a moderate who dramatically out-raised her. Can it carry her to victory in November?

© Saul Martinez for The New York Times

The Alaska Native, who grew up along the Kuskokwim River near the Bering Sea and fished for salmon, is the leading Democrat in the nonpartisan primary race.

© Ash Adams for The New York Times

The incumbent Republican has been a reliable supporter of President Trump, giving Democrats a pickup opportunity in a state where most are politically unaffiliated.

© Eric Lee/The New York Times

Senator Darline Graham made the remark in a debate against Representative Ralph Norman, her opponent in the runoff election to succeed her brother, Lindsey Graham. Here are five takeaways from the debate.

© Meg Kinnard/Associated Press

A burst of ad spending is part of a campaign tactic in which the major parties try to boost fringe hopefuls on the other side.

Nixon bested Alexander Vindman to win Democratic nomination and now faces Republican Ashley Moody in November

• Trump-backed Byron Donalds wins Republican primary in race to succeed Florida governor DeSantis

In an upset for the Democratic establishment, progressive Angie Nixon won the party’s US Senate primary in Florida, beating former army intelligence officer Alexander Vindman.

Nixon, a state representative and member of the Democratic Socialists of America, had significantly less funding going into the primary – with $975,000 to Vindman’s $16.3m at the end of July, according to Florida Politics.

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© Photograph: Dave Decker/ZUMA Press Wire/Shutterstock

© Photograph: Dave Decker/ZUMA Press Wire/Shutterstock

© Photograph: Dave Decker/ZUMA Press Wire/Shutterstock

Angie Nixon faces another difficult test this November against a Republican incumbent heavily favored to win.

© Saul Martinez for The New York Times