Peter Meijer, the one-term Republican congressman who lost his seat after voting to impeach President Donald J. Trump, has announced he is running for Senate in Michigan, jumping into a crowded primary in a key battleground.

“We are in dark and uncertain times, but we have made it through worse,” Mr. Meijer said in a statement announcing his candidacy on Monday.

Mr. Meijer, an heir to the Meijer supermarket empire and an Army Reserve veteran who served in Iraq, joins a field that includes Mike Rogers, another former representative who served seven terms in the House and led the House Intelligence Committee, who announced his candidacy in September.

Also running in the Republican primary are James Craig, former chief of the Detroit Police Department; Nikki Snyder, a member of the State Board of Education; Dr. Sherry O’Donnell, a physician and former 2022 congressional candidate; Sharon Savage, a former teacher; Ezra Scott, a former Berrien County commissioner; Alexandria Taylor, a lawyer; J.D. Wilson, a technology consultant; and Michael Hoover, a businessman.

The crowded Republican field reflects a party eager to make gains in Michigan after Democrats swept to victory in the state in 2022. Gov. Gretchen Whitmer handily won re-election that year, part of a political trifecta as Democrats won total control of the state government.

President Biden narrowly won in Michigan in 2020 and the state is considered a battleground in next year’s presidential election.

Mr. Meijer, 35, is competing for the seat held by Senator Debbie Stabenow, a Democrat who announced this year that she would not seek a new term in 2024. The race for the open seat is competitive but has been leaning toward the Democrats, according to a projection by the Cook Political Report.

Ms. Stabenow’s retirement set off a frenzy among ambitious Democrats in Michigan who are now aiming to succeed her.

Among them is Representative Elissa Slotkin, a moderate and former C.I.A. analyst who has earned a national profile and scored victories in several close races for her House seat. Also in the running are Nasser Beydoun, a businessman from Dearborn; Hill Harper, an author and actor; Leslie Love, a former state representative of Detroit; Pamela Pugh, the president of the State Board of Education; and Zach Burns, a lawyer and Ann Arbor resident.

Mr. Meijer was elected to represent his Grand Rapids-based district in 2020. He was thrust into the national spotlight just days after taking office when he voted to impeach Mr. Trump for inciting an insurrection on Jan. 6, 2021.

Only two of the 10 House Republicans who voted to impeach Mr. Trump survived the retribution from Republican voters that followed. Mr. Meijer narrowly lost his primary to a Trump-backed opponent, John Gibbs, who was boosted by Democrats and who was defeated by his Democratic opponent in the general election.

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