Representative Elise Stefanik, campaigning to oust Representative Liz Cheney as the Republican Party’s No. 3 leader in the House for calling out President Donald J. Trump’s election lies, pitched herself as an unshakable ally of the former president on Thursday, calling him the “strongest supporter of any president when it comes to standing up for the Constitution.”

In her first public interview since announcing she would run for Ms. Cheney’s post amid a drive by Republican leaders to force out the Wyoming lawmaker, Ms. Stefanik, of New York, appeared on Steve Bannon’s “War Room,” a hard-right program run by Mr. Trump’s former strategist, and promised to unite the party under the former president’s banner.

“My vision is to run with support from the president and his coalition of voters,” Ms. Stefanik said, referencing Mr. Trump, adding later that she was committed to “sending a clear message that we are one team, and that means working with the president and working with all of our excellent Republican members of Congress.”

Ms. Stefanik’s glowing comments about Mr. Trump captured the contrast between her and Ms. Cheney, who has relentlessly criticized the former president for falsely claiming the election was stolen and beseeched Republican lawmakers — most recently in a scathing opinion piece on Wednesday — to excise him from the party before it collapses into irrelevance.

“Trump is seeking to unravel critical elements of our constitutional structure that make democracy work — confidence in the result of elections and the rule of law,” Ms. Cheney wrote. “No other American president has ever done this.”

In the interview on Thursday, Ms. Stefanik, who voted to overturn the election results on Jan. 6 and has echoed Mr. Trump’s false claims of voter fraud, repeated some of those allegations, citing “unprecedented unconstitutional overreach” from state officials.

“These are questions that are going to have to be answered before we head into the 2022 midterms,” Ms. Stefanik said of the questions she raised about the legitimacy of President Biden’s victory.

Though Ms. Cheney beat back an effort in February to replace her as conference chair following her vote to impeach Mr. Trump, most Republicans — even her allies — expect her to be stripped of the position as early as next week. Top Republican leaders who backed her earlier this year have moved to support Ms. Stefanik.

And many of the party’s rank-and-file members, including some who agree with Ms. Cheney’s caustic assessments of Mr. Trump, say privately that have grown weary of her determination to continue publicly repudiating his lies and rebuking members of her own party for their role in fueling the falsehoods that inspired the Jan. 6. riot at the Capitol.