Several election deniers backed by former President Donald Trump prevailed in closely-watched primaries held Tuesday, as a nationwide battle over the future of the GOP played out in state and federal races across five states.

In Michigan, Rep. Peter Meijer, one of 10 House Republicans who voted to impeach Trump last year, fell in defeat to John Gibbs, a former Trump administration official who ran with the ex-president's support and embraced his false claims of a stolen election. Meijer, who is in his first term, becomes the second GOP House member ousted in a primary after supporting the impeachment of Trump for inciting a riot with false claims of a stolen election. Meijer issued a statement conceding before the race was called.

In Arizona, state lawmaker Mark Finchem - part of a national coalition of far-right candidates who baselessly reject the 2020 election results and want to oversee the vote in 2024 - was projected to win the Republican nomination for GOP secretary of state. Blake Masters, a first-time candidate who spent most of his career in Silicon Valley as a protégé of tech billionaire Peter Thiel and has said he thinks Trump won in 2020, was projected to win the Republican nomination for U.S. Senate in the state. Both were backed by Trump.

A third Arizona candidate supported by Trump, former TV news anchor Kari Lake, was in a close race for the GOP gubernatorial nomination that had yet to be called by the Associated Press early Wednesday morning. In close competition was Karrin Taylor Robson, who has the support of Republicans who rebuffed Trump's pressure to interfere with the 2020 election - including former Vice President Mike Pence.

And in Missouri, Attorney General Eric Schmitt won his state's GOP nomination for U.S. Senate - a relief to Republicans who had feared his scandal-plagued rival Eric Greitens would imperil an otherwise safely red seat and become a broader political problem for the party. As attorney general, Schmitt backed a Texas-led lawsuit seeking to overturn the 2020 election results in four key states Trump lost. Trump issued a unusual endorsement on the eve of the primary, announcing support for "ERIC," a first-name shared by two rival candidates.

State and federal races in these states as well as Kansas and Washington state kicked off a final series of intraparty contests before the midterms that will determine control of Congress in the fall. It was unclear what the totality of Tuesday's primaries would reveal about the influence of Trump and his ideas, with key contests yet to be settled. Two other Republicans who voted to impeach Trump - Reps. Jaime Herrera Beutler and Dan Newhouse in Washington state - were also hoping Tuesday to fend off Trump-backed challengers who baselessly reject the 2020 results.

Meanwhile in Kansas, voters rejected a constitutional amendment that would have imperiled abortion access in the state. The vote was the first electoral test of the issue since the Supreme Court in June overturned a national right to abortion established in Roe v. Wade.

Trump's record has been mixed in this year's primary season, with voters in some states embracing his preferred candidates and others rejecting them. His endorsed candidates on the ballot Tuesday embraced his combative style, with at least one seeking to portray herself as the winner before the Associated Press had made a call in her contest.

As she trailed in initial results, Lake greeted supporters on stage where she sought to claim victory and continued her attacks on Arizona's election systems. When she takes office, she told the hundreds gathered, she would reform the way Arizonans voted. "There is no path to victory for my opponent and we won this race," she said to cheering supporters.

Down the ballot, Arizona House Speaker Rusty Bowers lost to former state Sen. David Farnsworth in a GOP primary for a state Senate district. Bowers says Trump lost the election, while Farnsworth says he is convinced he did not. Bowers also testified on Capitol Hill about efforts by Trump and his allies to press him to undo a close defeat in Arizona.

While GOP primaries took much of the spotlight Tuesday, Democratic divisions were also on display. In Michigan's redrawn 11th Congressional District, Rep. Haley Stevens was projected to defeat Rep. Andy Levin. A pro-Israel super PAC - a major spender against left-wing candidates in Democratic primaries - invested millions to beat Levin, who unlike Stevens is Jewish.

In Missouri, Republican leaders' opposition to Greitens intensified this summer after he released a threatening ad in which he wielded a shotgun and encouraged supporters to get a "RINO hunting permit" - a reference to "Republicans in name only." Party leaders urged Trump not to endorse the candidate, who has been accused of domestic abuse.

Trump signaled Monday he would weigh in at the last minute - then announced his support for "ERIC," leaving voters to choose between two people who had clamored for his approval.

With more than 90% of the vote counted in Missouri, Schmitt led at about 46%, according to the Associated Press. Rep. Vicky Hartzler, R-Mo. - who had the endorsement of Sen. Josh Hawley, R-Mo. - got about 22% , while Greitens trailed at 19%.

Greitens resigned from the governor's office in 2018 amid accusations of sexual misconduct and other scandals. He acknowledged having an affair but denied other allegations, and an investigation found no wrongdoing on a campaign finance charge. In March, Greitens's ex-wife also said he knocked her down and left one of their children with a loose tooth. Greitens denied the allegations as some Republicans in Congress urged him to withdraw from the Senate race.

Trudy Busch Valentine, a philanthropist and heiress to a brewery company fortune, was projected to win the Democratic nomination for Senate in Missouri.

In Michigan, the Democratic Congressional Campaign Committee has spent nearly half a million dollars boosting Gibbs - gambling that he would be easier to defeat in a district that leans slightly blue. The move drew cries of hypocrisy across parties, even as Democrats widely hope that Republicans' embrace of extremes will hurt them in the fall.

Some Republicans also fear Trump's picks in battleground areas could undermine their party's chances in November, as they seek to capitalize on low approval ratings for Biden, rising inflation and concerns about crime.

Nancy Miller, 58, said she voted two years ago for Meijer but soured on him when he voted to impeach Trump after the former president's supporters stormed the U.S. Capitol on Jan. 6, 2021.

"Meijer messed up, I think," Miller said. "I was like, what did he do? Dumb, dumb, dumb!"

Four other House Republicans who voted to impeach Trump last year opted not to run for reelection, while Rep. Tom Rice, R-S.C., lost his primary to a Trump-backed critic earlier this summer. Rep. David Valadao advanced from his all-party primary in California, where Trump declined to endorse a challenger and some Republicans saw Valadao as their best candidate to retain a blue-leaning seat.

Herrera Beutler and Newhouse entered the day with potentially better chances of beating back Trump-endorsed candidates because of Washington's primary system, in which the two candidates with the most votes advance to the general election regardless of party. Former Army officer Joe Kent was challenging Herrera Beutler from her right, while former police chief Loren Culp was hoping to unseat Newhouse.

Beyond the congressional contests, strategists in both parties were also watching a statewide race in Michigan, where former conservative commentator Tudor Dixon won the GOP nomination for governor and will face Gretchen Whitmer, one of several Democratic governors seeking reelection this fall in swing states.

Dixon got Trump's endorsement late in the race and indicated at a debate this spring that she did not believe Biden won her state in 2020. But other contenders for the GOP nomination recently attacked her as insufficiently loyal to Trump's insistence the election was "stolen."

Trump also endorsed 11 state legislative candidates in Michigan - more than any other state - setting up proxy wars with his former Cabinet member Betsy DeVos and Rep. Adam Kinzinger, R-Ill., who have both criticized Trump's conduct during the storming of the Capitol.

Some of the starkest tests of Trump's influence Tuesday were playing out in Arizona, an epicenter of Trump allies' continuing efforts to question and overturn the election. Republican state lawmakers sanctioned a months-long "audit" of the vote in Maricopa County, a spectacle that affirmed Biden's win but provided new fuel for wild and baseless theories of wrongdoing.

Masters and Ohio GOP Senate nominee J.D. Vance are some of the highest-profile figures in a "New Right," preaching economic populism, nationalism and conservative social values. Both have promised to take on Big Tech despite their ties to its elite world. Masters said in an early campaign ad that "Trump won" in 2020 and pitches himself as a fighter in a culture war against the "woke" left.

The GOP gubernatorial primary in Arizona became a proxy war between Trump and conservatives who want to move on from his endless election grievances. Trump last year backedLake, who says the 2020 election was stolen and rails against the media and the GOP establishment; his old running mate Pence more recently endorsed Taylor Robson, a developer with support from the party's more traditional, pro-business wing.

Trump and Pence also issued dueling endorsements this spring in Georgia - where Republican Gov. Brian Kemp overcame a Trump-led campaign of retribution for certifying the 2020 election results. Pence, too, broke with Trump after refusing to overturn the election and alluded in Arizona last month to "those who want to make this an election about the past."

With his Arizona endorsement, Pence waded into a highly competitive race - a contrast to Georgia, where Kemp was long favored to win. Arizona Gov. Doug Ducey (R), a friend of Pence's, also backed Taylor Robson, who gained momentum late in the race while spending $15 million of her own money. Taylor Robson and Lake have both sought to undermine each other's conservative credentials, with Taylor Robson highlighting Lake's past support for former president Barack Obama.

Lake could chip away at Taylor Robson's lead as more in-person votes are counted, political observers said, because of her supporters' heightened distrust of early mail voting. Whoever prevails will face Arizona Secretary of State Katie Hobbs (D), who beat two other candidates in the Democratic primary and has been a prominent voice against efforts to undermine faith in Arizona's elections.

Finchem and Lake - who would also sign off on election results as governor - have both advocated drastic changes to voting in Arizona, at one point seeking to ban voting machines and count all ballots by hand. Finchem has also been subpoenaed by the House committee investigating the Jan. 6, 2021, attack on the Capitol. He was photographed outside the Capitol that day, in the thick of a crowd; Finchem has said he did not enter and has not been charged in the attack.

"This could be the last time we have free and fair elections," said Adrian Fontes, who oversaw voting in Arizona's biggest county in 2020 and was in a tight race Tuesday night with Arizona Democratic Rep. Reginald Bolding in the Democratic primary for secretary of state. Fontes and other Democrats are alarmed by the candidates advancing in Republican primaries as well as the Supreme Court's recent move to consider a conservative legal argument that could give state legislatures new power to shape and reject election results.

Maria Kupillas, an independent voter from Scottsdale, Ariz., said she "felt a little defeated" after casting a Republican ballot Tuesday.

"The choices were bad to worse, so it didn't give me a lot of hope for who's actually going to be elected in November," said Kupillas, a trial attorney. When she moved to Arizona in 2004, she thought of it as "purple and moderate" - the state that elected the late John McCain. "I feel like Arizona, sadly, is going in the far-right direction," she said.

Trump may have paved the way for the success of a slew of populist, anti-establishment candidates, said Stan Barnes, a former state lawmaker and GOP strategist in Arizona - but he argued that "Donald Trump could be hit by a bus and that fervor would not subside."

On the Democratic side, two of Congress's most liberal members, Rep. Cori Bush, D-Mo., and Rep. Rashida Tlaib, D-Mich., faced more moderate challengers Tuesday. Bush was projected to win. Bush and Tlaib are part of a group of mostly female lawmakers of color known as "the Squad."

In Kansas, Republican state Attorney General Derek Schmidt was projected to win the GOP nomination to challenge Democratic Gov. Laura Kelly, who easily advanced, according to the Associated Press. Kelly defeated Republican Kris Kobach in 2018 despite her state's conservative bent.

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The Washington Post's Yvonne Wingett Sanchez in Arizona, Kathy Gilsinan in Missouri, Dave Weigel in Washington and Patrick Marley in Michigan contributed to this report.