Three Republican U.S. House members who voted to impeach President Trump over the events of January 6, 2021, are being challenged in Tuesday’s primary elections by rivals endorsed by the former president.

The primaries for Representatives Peter Meijer, Jaime Herrera Beutler, and Dan Newhouse are the biggest test yet for GOP incumbents who broke with Mr. Trump after a mob of his supporters stormed the U.S. Capitol in a bid to keep him in power. Mr. Trump has vowed revenge against the 10 House Republicans who crossed party lines for the impeachment vote.

Of the 10, four opted not to run for re-election in this year’s midterm elections. As for the ones who did, Representative Tom Rice of South Carolina lost to a Trump-endorsed challenger in June, while Representative David Valadao of California survived a challenge that same month from a fellow Republican, advancing to the general election. Representative Liz Cheney of Wyoming is bracing for defeat in her August 16 primary against a Trump-backed rival.

In other races Tuesday, two Democratic incumbents in Michigan are facing each other in a newly drawn congressional district, and two members of the “Squad” have primary challengers, in Missouri and Michigan. In Arizona, GOP voters will decide whether to nominate a major QAnon figure for a congressional seat.

Some of the top elections:

FACING VOTERS AFTER IMPEACHMENT VOTES

The three House Republicans facing primary challenges Tuesday for impeaching Mr Trump say they don’t regret their vote.

In Michigan, Mr. Meijer voted for impeachment just days after he was sworn into office for his first term. The former president has endorsed Mr. Meijer’s opponent, John Gibbs, a businessman and missionary who served in the Trump administration under the housing secretary, Ben Carson.

Mr. Gibbs has contended Mr. Meijer is not a true Republican because he voted to impeach Mr. Trump, and Mr. Gibbs chastised Mr. Meijer for supporting bipartisan gun control legislation that President Biden signed into law in June.

Mr. Meijer, a member of the Army Reserves who served in Iraq, has criticized Mr. Biden over the U.S. withdrawal from Afghanistan, as well as his handling of the economy. The congressman’s family is well known in the Midwest as owners of the chain of Meijer grocery megastores, and he has a large fundraising advantage over Mr. Gibbs. The winner will face Democrat Hillary Scholten in November in the state’s Democratic-leaning 3rd Congressional District.

In Washington state, the two Republicans who voted for impeachment are competing in crowded primaries, from which the top two vote-getters, regardless of political party, will move on to the general election in November.

Ms. Herrera Beutler’s primary against eight challengers, four of whom are Republicans, in Washington state’s 3rd Congressional District will be one of the toughest of her career. Mr. Trump is backing Joe Kent, a former Green Beret who has promoted the former president’’s lies that the 2020 election was stolen.

Ms. Herrera Beutler has been in Congress since 2011 and represents an area that has favored Republicans.

In the central part of Washington, Mr. Newhouse, a four-term congressman, is facing seven challengers, six of whom are Republicans, in the solidly conservative 4th Congressional District. His rivals include Loren Culp, a former small-town police chief who refused to concede the governor’s race in 2020. Mr. Culp has Mr. Trump’s backing but has lagged other candidates in fundraising.

CANDIDATE LINKED TO QANON

Ron Watkins, one of the most prominent figures in the QAnon conspiracy movement, is running for a House seat in Arizona’s sprawling 2nd Congressional District.

He served as the longtime administrator of online message boards that helped seed the conspiracy movement whose adherents believe a group of satanic, cannibalistic child molesters secretly runs the globe.

Mr. Watkins no longer runs the message boards and has denied fueling the QAnon movement. He said he is running for Congress because he hopes to “fix the machine from the inside.”

He is considered a long shot in the crowded GOP field, having been outpaced in campaign fundraising by the other candidates.

A state representative, Walter Blackman, and a former Navy SEAL who owns a bottle opener business and was endorsed by Mr. Trump,  Eli Crane, are considered the leading GOP contenders. The winner will take on the Democratic U.S. representative, Tom O’Halleran, in November in a district that favors Republicans.

FROM COLLEAGUES TO COMPETITORS

Two incumbent Michigan Democrats, Representatives Andy Levin and Haley Stevens, are running against each other for a newly drawn 11th Congressional District in suburban Detroit. They’re vying for a left-leaning area, which means the winner of Tuesday’s contest will likely win the seat in November.

Ms. Stevens flipped a district in 2018 that was long held by Republicans. Before running for office, she led the auto bailout under President Obama.

Mr. Levin also won his first term in 2018, taking over the seat long held by his father, Representative Sander “Sandy” Levin. He’s been endorsed by Senators Sanders and Warren.

CHALLENGING THE ‘SQUAD’

Two members of the “Squad” in Congress are facing primary challenges on Tuesday.

In Michigan, Representative Rashida Tlaib faces three Democratic challengers as she seeks a third term in office. She’s running in a newly drawn Detroit-area district where the winner is expected to easily carry the 12th Congressional District seat in November. Ms. Tlaib’s main competition is a longtime Detroit city clerk, Janice Winfrey, who has strong name recognition in the city.

In Missouri, a first-term representative, Cori Bush, is facing a challenge in the state’s 1st Congressional District. A state senator, Steve Roberts, is betting that Ms. Bush, a vocal advocate for defunding the police and moving money to social services and mental health programs, is too liberal even for heavily Democratic St. Louis.

Mr. Roberts has twice faced rape allegations, though prosecutors said they didn’t have enough evidence to merit charges. He has accused the Bush campaign of dredging up the allegations to distract from her record.

Ms. Bush has touted her accomplishments, including persuading the Environmental Protection Agency to clean up radioactive waste near a St. Louis County creek, pushing for climate change action, and standing against evictions during the COVID-19 pandemic.

10 YEARS AFTER SHOOTING, INTERN SEEKS GIFFORDS SEAT

Daniel Hernandez Jr., the hero intern credited with saving Representative Gabrielle Giffords’s life after an attempted assassination in 2011, is running for her former seat in Congress.

Mr. Hernandez, who recently stepped down from the state legislature to focus on his campaign, faces another former lawmaker in the Democratic primary. However, the once highly competitive district centered in Tucson now favors Republicans after the boundaries were redrawn.

Mr. Hernandez was a 20-year-old college student in his first week interning for Ms. Giffords when he went to her “Congress on your corner” constituent event. A gunman there opened fire, killing six and injuring 13. Mr. Hernandez kept the Democratic congresswoman conscious and applied pressure to her head wound until paramedics arrived.

By Michelle L. Price. Sara Burnett, Felicia Fonseca, Joey Cappelletti, Jonathan J. Cooper, Chris Grygiel, and Jim Salter contributed to this report.