Trump via Twitter claimed victory in one nevertheless.

In battleground Ohio, the president took credit for Republican Troy Balderson's performance, calling it "a great victory," even though the contest could be headed to a recount.

Democrats could also celebrate their showing in a seat that has been held by the Republicans since 1983.

"We're not stopping now," Democrat Danny O'Connor told cheering supporters. He'll reprise his campaign against Balderson from now through November's general election.

In deep-red Kansas ' Republican gubernatorial primary, the candidate Trump backed on the eve of the election, Secretary of State Kris Kobach, was neck and neck with current Republican governor Jeff Colyer.

The day's races in five states, like many before them, tested the persistence of Trump's fiery supporters and the momentum of the Democratic Party's anti-Trump resistance.

After polling closed in the four states - Kansas, Michigan, Missouri and Washington - it became clear women had broken records for gubernatorial and House nominations.

Victories for Gretchen Whitmer (Michigan) and Laura Kelly (Kansas) in Democratic primaries mean 11 women will contest governorships in November - one more than the previous 1994 record.

At least 173 female major party nominees will run for the House, beating the record of 167 from 2016.

Former Michigan state lawmaker Rashida Tlaib won the Democratic nomination to run unopposed for a House seat, setting her up to become the first Muslim woman elected to Congress.

No Republicans or third-party candidates ran in Tuesday's District 13 primary race, meaning Tlaib is set to win the seat in November's election.

She would take the spot held since 1965 by John Conyers, who stepped down in December citing health reasons amid charges of sexual harassment.

Australian Associated Press