Pennsylvania state Senator Doug Mastriano, who has amplified Trump's false claims of 2020 voter fraud, will face Democratic Attorney-General Josh Shapiro in a high-profile governor's race.

In Pennsylvania's US Senate race, Lieutenant Governor John Fetterman won the Democratic nomination despite having been hospitalised since Friday after suffering a stroke.

Fetterman, a progressive Democrat whose victory over centrist US congressman Conor Lamb came just hours after he had a pacemaker implanted to address the irregular heart rhythms that caused the stroke, has said doctors expect a full recovery.

His Republican opponent remains to be decided, with TV wellness celebrity Mehmet Oz - endorsed by Trump - deadlocked with former hedge fund executive David McCormick as counting continues.

"If you'll allow me to be brutally honest for a second, 2022 is going to be hard year for Democrats," the tattooed, goateed Fetterman, who prefers shorts and hoodies to suits, said in an fundraising email to supporters. "A typical Democrat running a typical campaign isn't going to win."

In North Carolina, US congressman Madison Cawthorn, backed by Trump, conceded defeat to a rival Republican in a closely watched primary after a series of scandals, according to media reports. Another Trump-endorsed candidate, US Representative Ted Budd, won the state's Republican US Senate nomination.

The Pennsylvania and North Carolina Senate races are two of the most important contests in the November 8 elections, as President Joe Biden's fellow Democrats fight to retain their slim majorities in the House of Representatives and Senate. Both seats are held by retiring Republican senators.

Budd, who beat former Governor Pat McCrory, will face Democratic former state Supreme Court Chief Justice Cheri Beasley, who handily won her party's nomination in the race to succeed Senator Richard Burr.

Cawthorn, a staunch Trump ally who at age 26 is the youngest member of the House, acknowledged his loss to Senator Chuck Edwards late on Tuesday.

Cawthorn drew criticism from fellow Republicans after a string of embarrassing episodes, including claiming that conservative leaders invited him to a cocaine-fuelled orgy, attempting twice to bring a gun onto a plane and having a video surface that showed him nude and gyrating against someone.

Republicans are well positioned to regain control of the House, which could enable them to frustrate Biden's legislative agenda. Democrats have a better chance of keeping control of the Senate, currently split 50-50 between the parties with Vice-President Kamala Harris holding the tie-breaking vote.

Australian Associated Press