A Trump-endorsed congressional candidate has won the Republican primary in West Virginia, while the former president’s favored candidate fell short in Nebraska’s primary election for governor.

Alex Mooney on Tuesday beat fellow incumbent David McKinley in West Virginia’s second congressional district Republican primary on Tuesday.

“Donald Trump loves West Virginia, and West Virginia loves Donald Trump,” Mooney said in his victory speech.

McKinley was sharply criticized by the former president when he broke with his party as one of 13 Republicans to vote with the Democrats to support Joe Biden’s $1.2tn infrastructure bill. Trump called McKinley a Rino, or “Republican in Name Only”, and endorsed Mooney the day Biden signed the infrastructure law.

The two incumbents, who have taken dramatically different approaches to their time in office, were pitted against each other in the state’s second congressional district after population losses cost West Virginia a US House seat.

In Nebraska, Trump’s choice for governor, Charles Herbster, lost to an official at a university, according to US media reports, even though Trump had hosted a rally for him a little more than a week earlier.

The Nebraska contest had been dominated in recent weeks by accusations that Herbster, an agriculture executive, had sexually harassed several women, which he has denied.

US media outlets projected rival Jim Pillen, a hog farmer and university board member, would defeat Herbster and win the nomination.

Also in Nebraska, Representative Don Bacon was on track to win the Republican primary after Edison Research predicted he would hold off challenger Steve Kuehl. Trump had urged voters to reject Bacon due to his criticism of Trump’s role in the January 6 2021 attack on the US Capitol. Bacon will face a competitive November election in the Omaha-based district against Democrat Tony Vargas, who was projected by Edison Research to win his party’s primary.

The races in Nebraska and West Virginia have provided some measure of the former president’s enduring sway with GOP voters. They come on the heels of a victory in Ohio by JD Vance, author of the bestselling memoir “Hillbilly Elegy”, who defeated six other candidates to win the Republican primary for US Senate last week. Vance was also endorsed by Trump.

The former US president is facing some of the biggest tests of his influence in Republican primary elections later this month. In Pennsylvania, his endorsed Senate candidate, Dr Mehmet Oz, is locked in a competitive race against former hedge fund CEO David McCormick and five others, while his candidate in North Carolina, US representative Ted Budd, is competing in a field that includes a dozen other Republicans.

In Georgia, Trump has endorsed primary challengers to governor Brian Kemp and secretary of state Brad Raffensperger, both of whom defied him by rejecting his false claims of voter fraud in the 2020 election.

In a story last month, the Nebraska Examiner interviewed six women who claimed Herbster had groped their buttocks, outside of their clothes, during political events or beauty pageants. A seventh woman said Herbster once cornered and forcibly kissed her.

In Nebraska, the allegations against Herbster, a longtime supporter of Trump’s, didn’t stop the former president from holding a rally with him earlier this month.

“I really think he’s going to do just a fantastic job, and if I didn’t feel that, I wouldn’t be here,” Trump said at the rally at a racetrack outside Omaha.

Some voters said the allegations didn’t dissuade them from backing Herbster either.As she voted at an elementary school in northwest Omaha on Tuesday, Joann Kotan said she was “upset by the stories, but I don’t know if I believe them”. Ultimately, the 74-year-old said she voted for Herbster “because President Trump recommended him”.

The Associated Press contributed reporting