LAS VEGAS (AP) — Adam Laxalt, a former state attorney general who has embraced lies about the 2020 election, won the Republican nomination for a pivotal Nevada Senate seat, fending off a challenge from a political newcomer and setting up what will likely be a fierce and costly race against incumbent Catherine Cortez Masto, one of the most endangered Democrats in an evenly divided Senate.

Laxalt enjoyed the backing of the Republican Party’s most influential figures, ranging from former President Donald Trump to Senate GOP Leader Mitch McConnell and Florida Gov. Ron DeSantis. But a late-stage challenge from political newcomer Sam Brown forced Laxalt to spend heavily in the final weeks of the primary campaign and tap into the support of some of his high-profile backers, particularly those with ties to Trump.

The matchup against Cortez Masto comes at a difficult moment for Democrats, weighed down by President Joe Biden’s low approval ratings and seeking to maintain control of Congress as people throughout the U.S. grapple with rising prices of everyday goods and gasoline. Republicans see the race as their best opportunity to flip a Senate seat and regain the majority, but are also watching for longer-term signals that Nevada is swinging back in their direction after rejecting every GOP presidential candidate since 2004.

“Together we have taken an important step tonight,” Laxalt said at a party in Reno, Nevada. “An important step in taking our country back, an important step in taking our great state of Nevada.”

Beyond the Senate race, Republicans in Nevada also picked Joe Lombardo as their nominee to challenge incumbent Democratic Gov. Steve Sisolak in what could be one of the most competitive governor’s races this year. And the GOP backed Jim Marchant as their candidate for secretary of state. A former state lawmaker, he has repeated false claims about the presidential campaign and, if elected, would be in charge of elections in a state that could be critical in determining the winner of the White House in 2024.

Nevada was one of several states that held elections Tuesday, about midway through a primary season that could reshape American politics. The results offered warnings for both parties.

In south Texas, Democrats lost a long-held seat in the U.S. House. They are likely to regain it in November, but Tuesday’s results were a reminder that the party’s standing is at risk of slipping among Latinos.

Trump, meanwhile, helped a South Carolina state lawmaker take out five-term incumbent Rep. Tom Rice, who backed the former president’s second impeachment last year. While the win could help Trump regain momentum after setbacks in a series of races last month, it happened in a rural, solidly Republican congressional district. Another incumbent that the former president sought to defeat in a neighboring district, Rep. Nancy Mace, held back the challenger, attracting some of the suburban moderates who bolted from the GOP during the Trump era.

Speaking to reporters after the results came in, Mace sought to strike a tone of consensus, pledging to “work with anyone who’s willing to work with me, full stop.”

For his part, Trump posted a statement on his social media platform saying Mace’s challenger, Katie Arrington, was a “long shot” who ran a “great race.” He offered his congratulations to Mace, who he said should easily prevail over a Democrat in the fall.

Still, much of the attention Tuesday was on Nevada.

Laxalt entered the primary with strong name recognition after serving for four years as Nevada’s attorney general. The grandson of former U.S. Sen. Paul Laxalt, he campaigned unsuccessfully for governor in 2018.

But perhaps most importantly in GOP circles, he's got ties to Trump. Laxalt worked on Trump's reelection campaign and promoted his lies about election fraud in the state after the 2020 election, including spearheading legal challenges to the vote-counting process. Trump in turn hosted Laxalt for a fundraiser at his Mar-a-Lago club in Palm Beach, Florida, and appeared in a campaign ad for Laxalt.

Trump’s false claims of fraud in the 2020 election were laced throughout the campaign. Last fall, Laxalt began raising fears of voter fraud in 2022 and talked about preemptively mounting legal challenges “to try to tighten up the election.”

Laxalt had insisted in 2020 that ineligible and dead voters cast ballots in the presidential election in Nevada, despite the state’s Republican secretary of state insisting that the results showing Biden’s victory were accurate and reliable.

Brown, to the surprise of many in the state, won the endorsement of the Nevada Republican Party at a convention vote in late April and a straw poll of the Las Vegas-area GOP at a May gathering. Recent polls showed him closing in on Laxalt, though the state, with a transient population and many late-shift workers due to the state’s tourism and casino industry, is considered fickle for pollsters.

Laxalt is now focused on trying to defeat Cortez Masto, the first Latina elected to the Senate and successor of the late Sen. Harry Reid. She is making her first reelection bid as Democrats broadly are facing headwinds this year, particularly when it comes to the economy. In Nevada, high prices for gas are acutely felt by residents of Las Vegas’ sprawling suburbs or those commuting from far-flung rural areas.

Those same factors could imperil the reelection of Nevada's Democratic governor, Sisolak. He will face Lombardo, the sheriff of Clark County, who also earned a coveted endorsement from Trump.

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Price reported from Washington. Associated Press writers Jill Colvin in New York, Meg Kinnard in Charleston, South Carolina and Gabe Stern in Reno, Nevada, contributed to this report.

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Michelle L. Price And Ken Ritter, The Associated Press