In Washington State, a House Republican who voted to impeach Trump concedes her race.

Representative Jaime Herrera Beutler of Washington, a Republican who voted to impeach former President Donald J. Trump and sharply criticized his actions leading up to the Jan. 6, 2021, attack on the Capitol, conceded her primary Tuesday in a crowded race that included a Trump-backed challenger and other 2020 election deniers.

“Thank you, Southwest Washington, for entrusting me six times with the privilege of representing you in Congress,” she said in a statement, a week after polls closed in Washington State. “Though my campaign came up short this time, I’m proud of all we’ve accomplished together for the place where I was raised and still call home.”

Marie Perez, a Democrat, and Joe Kent, the Republican endorsed by Mr. Trump, were leading in the race, which had not yet been called. The eventual winners will square off in November to represent Washington’s Third Congressional District, which encompasses the southwestern corner of the state.

Ms. Herrera Beutler is one of 10 House Republicans who voted to impeach Mr. Trump over the Jan. 6 insurrection. She is the third to lose in a primary, after Tom Rice of South Carolina and Peter Meijer of Michigan. Two others survived their primaries, and four declined to seek another term. The 10th, Representative Liz Cheney of Wyoming, faces a primary challenge next week.

Ms. Herrera Beutler’s eight opponents included three Trump loyalists who denounced her impeachment vote: Mr. Kent, a retired Special Forces officer; Vicki Kraft, a state representative; and Heidi St. John, a Christian author and co-founder of a home-schooling nonprofit.

All three have promoted false claims of voter fraud in the 2020 election.

Her Democratic opponent, Ms. Perez, is the owner of an auto repair shop in Portland and has made tackling rising health care costs and supporting workers and small businesses signature issues of her campaign.

Ms. Herrera Beutler should have been in a better political position than other Republicans who voted for impeachment because she represents a purple district in a deep-blue state. Washington’s “jungle” primary system — in which all candidates run on the same ballot and the top two, regardless of party, advance to the general election — could also have worked to her advantage by sparing her from a head-to-head contest with a Trump-aligned candidate.

Ms. Herrera Beutler was one of Mr. Trump’s most outspoken critics in the weeks after the Capitol attack. She called his actions inappropriate.

“My vote to impeach our sitting president is not a fear-based decision,” she said before casting it. “I am not choosing a side; I’m choosing truth. It’s the only way to defeat fear.”

The backlash was as swift as it was heavy. Republican Party officials in Washington vowed to support a more conservative candidate as a punishment for her impeachment vote. But Ms. Herrera Beutler had the support of Sam Reed, a Republican former secretary of state of Washington, and the largest Republican donor in her district, David Nierenberg.

Before the primary, she sought to stay focused on local issues, promoting legislation that passed the House to increase addiction treatment and mental health resources for residents in her district.

In her statement conceding the race, Ms. Herrera Beutler said some of her accomplishments as a legislator were pleasant surprises, such as growing her family and providing an example for mothers in elected office.

“And some were unexpected and difficult,” she added. “But I’m proud that I always told the truth, stuck to my principles, and did what I knew to be best for our country.”