Kari Lake, the former television anchor running for U.S. Senate in Arizona, will campaign on Thursday in Phoenix with a top Senate Republican, the latest sign of the party’s embrace of a candidate whose extreme views made her a lightning rod just two years earlier.

Ms. Lake and Senator John Barrasso of Wyoming, the No. 3-ranking member of Republican leadership, are expected to condemn President Biden for his handling of the migrant crisis, according to an adviser for Ms. Lake’s campaign, on the same day that both the president and Donald J. Trump, his predecessor and likely 2024 opponent, are in Texas visiting the southern border.

Not long ago, Republican leaders in Washington shied away from Ms. Lake, a bombastic ally of Mr. Trump who made echoing his false claims of fraud in the 2020 election a centerpiece of her 2022 campaign for governor, then spent more than a year challenging her own loss to her Democratic rival, Katie Hobbs, in court. She alienated establishment Republicans both in Arizona — with her attacks on the state’s former senator John McCain, who died in 2018 — and in Washington.

But just as Mr. Trump has emerged from a post-presidency nadir to seize a dominant position in the Republican presidential primary, Ms. Lake has begun to be embraced by some members of the Republican establishment as she mounts a bid for the Senate. She has adopted a more conciliatory tone and worked to get back in their good graces, courting the type of Republicans who shied away from her in 2022.

Chuck Coughlin, the chief executive of the Phoenix political consulting firm HighGround, suggested that Mr. Barrasso’s presence could help broaden Ms. Lake’s base of support. “He would be effective at speaking to an audience of Republicans and unaffiliated voters to persuade them to give Lake a second look,” he said.

Ahead of Arizona’s Republican Senate primary on July 30, Ms. Lake has led her primary challenger Mark Lamb, a sheriff, by wide margins in polls, and she scored a key endorsement this month from the National Republican Senatorial Committee, led by Senator Steve Daines of Montana. She has also attracted the support of Republican senators like J.D. Vance of Ohio and Rand Paul of Kentucky as the party seeks to seize control of the chamber via elections this fall.

Democrats are playing defense across the Senate map this cycle, with Arizona joining Montana, Nevada, Ohio, Pennsylvania and West Virginia as potential Republican pickups.

Republican leaders hope their support for Ms. Lake can bolster her in what is expected to be a tight race against her Democratic opponent in the general election, Representative Ruben Gallego, who is in Washington on Thursday with the House in session. Senator Kyrsten Sinema, who left the Democratic Party in 2022 and became an independent, has not yet said if she will run again for the seat, but faces an April 1 deadline to collect tens of thousands of signatures to qualify for the race.

In addition to the Phoenix event focused on the border, the pair will also attend a lunch devoted to a discussion of economic issues and inflation and make several stops at local restaurants and businesses to speak with voters. Mr. Barrasso will then headline a fund-raiser for Ms. Lake’s campaign in Paradise Valley, a Phoenix suburb.

The party has made the border crisis a key issue in 2024, even as Republicans in Congress this month tanked a bipartisan immigration deal that would have achieved many of their aims, such as making it more difficult to claim asylum and expanding detention capacity. After Mr. Trump came out against the deal, other Republicans — including Ms. Lake and Mr. Barrasso — followed suit, saying it was not stringent enough.