Minnesota congresswoman Ilhan Omar, a member of the select progressive group in the House of Representative dubbed the Squad, eked out a closer-than-expected Democratic primary victory on Tuesday night against a centrist challenger who questioned the incumbent’s support for the “defund the police” movement.

The evening went far smoother for another progressive, Becca Balint, who won the Democratic House primary in Vermont – positioning her to become the first woman representing the state in Congress.

But Tim Michels, backed by Donald Trump, was projected to win the Republican nomination for governor of Wisconsin, a day after the FBI searched the former US president’s home in Florida reportedly seeking classified documents.

Michels defeated rival and former lieutenant governor Rebecca Kleefisch, who had been endorsed by Trump’s former vice-president, Mike Pence.

Kleefisch served with right-wing former governor Scott Walker and she conceded to Michels on Tuesday night.

Michels has falsely asserted that Trump, rather than Democratic US president, Joe Biden, won the vital swing state in the 2020 presidential election, echoing the former president’s claims.

Michels has also vowed to enforce a 19th-century abortion ban that went into effect in Wisconsin after the US supreme court in June eliminated the nationwide right to the procedure with its overturning of the landmark Roe v Wade ruling.

He will face the incumbent Wisconsin governor and Democrat, Tony Evers, in November’s election.

With a Republican-majority legislature, Michels could push through new abortion restrictions if elected. Evers and his administration have filed litigation challenging the 1849 law while promising not to prosecute doctors who violate it.

Other Trump-backed candidates also prevailed.

In Connecticut, Leora Levy surprised observers by winning the Republican primary race for the US Senate after being supported by Trump, upending moderate Themis Klarides who had a lot of party support in the state, the Hartford Courant reported.

Levy faces the high-profile incumbent Democratic senator Richard Blumenthal.

In her Minneapolis district, Omar, who is one of the left’s leading voices in Congress, has defended calls to redirect public safety funding more into community-based programs.

She squared off with former city council member Don Samuels, whose north Minneapolis base suffers from more violent crime than other parts of the city.

Samuels argued that Omar is divisive and helped defeat a ballot question last year that sought to replace the city police department with a new public safety unit.

He and others also successfully sued the city to force it to meet minimum police staffing levels called for in Minneapolis’s charter.

But Omar narrowly prevailed on the night, seeking her third term in the House. She crushed a similar primary challenge two years ago from a well-funded but lesser-known opponent.

“She’s had a lot of adversity already and pushback. I don’t think her work is done,” said Kathy Ward, a 62-year-old property caretaker for an apartment building in Minneapolis who voted for Omar. “We’ve got to give her a chance.”

Two other members of the Squad – Rashida Tlaib of Michigan and Cori Bush of Missouri – won their Democratic primaries last week.

Meanwhile, Republicans see a pickup opportunity in Wisconsin’s third congressional district, the seat being vacated by the retiring Democratic incumbent Ron Kind.

The district covers a swath of counties along Wisconsin’s western border with Minnesota and includes La Crosse and Eau Claire.

Republican Derrick Van Orden was unopposed in his primary on Tuesday and has Trump’s endorsement.

Van Orden narrowly lost to Kind in the 2020 general election. He attended Trump’s rally near the White House on 6 January 2021, where the then president urged his supporters to “fight like hell” to overturn his election defeat by Joe Biden, but has said he never set foot on the grounds of the Capitol during the insurrection that followed.

State senator Brad Pfaff topped three other Democrats to secure the party’s nomination and will face Van Orden in the fall. Pfaff, a one-time state agriculture secretary, had previously worked for Kind and received his endorsement.

Vermont is the last state in the country yet to add a female member to its congressional delegation. Balint, who immediately becomes the favorite in November’s general election, would also be the first openly gay member of Congress from Vermont.

She was endorsed by some of the nation’s leading leftwing figures, including the Vermont senator Bernie Sanders, Massachusetts senator Elizabeth Warren and Representative Pramila Jayapal, chair of the Congressional Progressive Caucus.

“Vermont has chosen a bold, progressive vision for the future, and I will be proud to represent us in Congress,” Balint said in a statement.

Balint is vying to fill the state’s lone House seat, which is being vacated by Peter Welch who is running for Senate and easily secured the Democratic nomination on Tuesday.

Welch is trying to succeed retiring senator Patrick Leahy, the US Senate’s longest-serving member.