Former Representative Peter Meijer, who lost his Republican House primary last year after voting to impeach President Donald J. Trump, has formed an exploratory committee to run for Senate in Michigan.

Mr. Meijer filed paperwork with the I.R.S. this week and confirmed the creation of the committee — which allows him to raise money before formally declaring a campaign — in a text to The New York Times on Thursday. The news was previously reported by The Detroit Free Press.

If he moves forward, Mr. Meijer, 35, would be the first well-known Republican to enter the race for the seat held by Senator Debbie Stabenow, a Democrat who is not seeking re-election. But he may not be the last: Former Representative Mike Rogers, who served seven terms in the House and led the House Intelligence Committee before leaving in 2015, is widely expected to run as well.

Republicans see the race, in a swing state that Mr. Trump won in 2016 but lost in 2020 to Joseph R. Biden Jr., as a major opportunity in their effort to retake control of the Senate. They need to gain either one or two seats, depending on whether they win the White House.

“I am honored by the many Michigan conservatives who are encouraging me to run for Michigan’s open Senate seat,” Mr. Meijer said in a statement. “Winning in 2024 is the only way we can stop Biden’s ruinous economic policies and mass weaponization of government.”

“The unserious old guard establishment that left us in this mess can’t be trusted to secure the border, restore our economic might to beat the C.C.P. or repair America’s image abroad after Biden betrayed our Afghan allies,” he added, using initials for the Chinese Communist Party. “It will take someone who can’t be bought and is willing to be bold, and I am considering running for Senate to do my part to get us out of this mess.”

The reference to the United States’ withdrawal from Afghanistan recalled one of the non-impeachment-related headlines Mr. Meijer made in his short time in Congress: In August 2021, he and Representative Seth Moulton, Democrat of Massachusetts, flew to Kabul without authorization to assess evacuation efforts.

Mr. Meijer, an heir to the Meijer supermarket empire and a veteran of the United States Army Reserve who served in Iraq, was elected to Congress in 2020. He might have been seen as a rising star in the Republican Party if it weren’t for one of his first acts in office: voting to impeach Mr. Trump for “incitement of insurrection.”

A year and a half later, he narrowly lost his primary to a Trump-supporting opponent, John Gibbs. Democrats had intervened in the race on behalf of Mr. Gibbs, who they believed would be easier to defeat in the general election and whom they did ultimately defeat.

Of the 10 Republicans who voted to impeach Mr. Trump, only Representatives Dan Newhouse of Washington and David Valadao of California were re-elected in 2022. Mr. Meijer was one of four defeated in primaries, alongside Liz Cheney of Wyoming, Jaime Herrera Beutler of Washington and Tom Rice of South Carolina. Another four — Anthony Gonzalez of Ohio, John Katko of New York, Adam Kinzinger of Illinois and Fred Upton of Michigan — retired rather than face the Republican base again.

That history suggests Mr. Meijer will face an uphill battle in the Senate primary, particularly if other prominent candidates enter the race. At the moment, though, his opponents are lesser known: Nikki Snyder, a member of the Michigan State Board of Education; Ezra Scott, a former county commissioner; Michael Hoover, an entrepreneur; and Alexandria Taylor, a lawyer.

The Democratic field so far is headlined by Representative Elissa Slotkin, who was elected to Congress in the blue wave of 2018 and has won re-election twice in a swing district. Her primary opponents include Hill Harper, an actor; Nasser Beydoun, a businessman; and Pamela Pugh, the president of the State Board of Education.