J.D. Vance, a candidate for the US Senate who is backed by Donald Trump, has won the Republican primary vote in Ohio, in an early test of the former president’s sway over his party as he eyes a possible White House run in 2024.

Mr Trump upended the Ohio race last month by endorsing author and venture capitalist Mr Vance ahead of the November 8 congressional elections, catapulting him ahead of former state Treasurer Josh Mandel, also a staunch Trump supporter.

With about 68 per cent of expected ballots counted, Mr Vance led the Republican field with 32 per cent of the vote, followed by Mr Mandel with 24 per cent and state politician Matt Dolan with 22 per cent, according to Edison Research.

While Mr Vance’s victory is a sign of Mr Trump’s endorsement power, every other major candidate besides Mr Dolan had lobbied hard for Mr Trump’s support while advocating for his policies and parroting his false claims of widespread fraud in the 2020 election.

“It was a big night for Trumpism in the Ohio Republican Party. Not just in Vance’s win but in a field that was dominated by candidates trying to out-Trump each other,” said University of Cincinnati political science professor David Niven.

“It was still a close race. He wasn’t able to shut this race down with a simple wave of his magic wand.”

Mr Vance, author of the Hillbilly Elegy book and a former Trump critic, will face Democratic US Representative Tim Ryan, who won his Senate primary as had been expected.

“I have absolutely got to thank the 45th, the president of the United States, Donald J. Trump,” Mr Vance told the crowd at his primary night party in Cincinnati.

Mr Trump has not announced his plans for 2024, but regularly hints at his political rallies that he intends to mount another presidential campaign.

Mr Ryan, who briefly ran for president in 2020, has focused his campaign on working-class voters, which has included taking a hardline on China and courting Trump supporters.

“I want us to be the manufacturing powerhouse of the world. I want us to help this country leapfrog China,” Mr Ryan told a gathering of supporters after sealing the nomination.

“We can do it by coming together.”

A rematch between two Democratic rivals for a US House seat was also on the ballot in Ohio on Tuesday, while voters in Indiana also cast primary ballots.

Tuesday’s contests kicked off a series of critical nominating contests in the coming weeks, including primaries in North Carolina, Pennsylvania and Georgia.

Mr Trump has endorsed more than 150 candidates, including about a dozen key picks.

His involvement will help determine whether Republicans, as expected, reverse their slim deficit in the House and also possibly take control of the Senate, which is split 50-50 with Democrats owning the tie-breaking vote.

A loss of control of either chamber would allow Republicans to block Mr Biden’s legislative agenda and also to pepper his administration with distracting and potentially politically damaging investigations.

– AAP