By Andy Sullivan and Jason Lange

WASHINGTON (Reuters) -A West Virginia candidate for U.S. Congress backed by Donald Trump was projected to win his Republican primary contest on Tuesday, while voters in Nebraska rejected the former president's request to unseat an incumbent House Republican.

Tuesday's elections are part of a series of nominating contests that will set the stage for Nov. 8 elections in which Republicans are favored to win control of at least one chamber of Congress, which would give them the power to bring Democratic President Joe Biden's legislative agenda to a halt.

In West Virginia, Edison Research projected that Alex Mooney, Trump's preferred candidate, would defeat rival David McKinley. The unusual race pits two incumbent Republicans in the U.S. House of Representatives against each other in a mountain state that has lost a seat due to its shrinking population.

In Nebraska, U.S. Representative Don Bacon, who Trump urged voters to reject due to his criticism of Trump's role in the Jan. 6, 2021 attack on the U.S. Capitol, held off challenger Steve Kuehl.

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.

Trump has endorsed more than 150 candidates this year as he lays the groundwork for a possible presidential bid in 2024. His influence will be put to the test in high-profile Senate contests later this month in Pennsylvania, North Carolina and Georgia.

The congressional race in West Virginia pitted Mooney, who has backed the former president's false accusations of fraud in the 2020 election, over McKinley, who was backed by Governor Jim Justice.

McKinley campaigned on his support for Biden's infrastructure package, which will send billions of dollars in new spending for roads, bridges and other projects to the low-income state. Mooney, like most House Republicans, voted against the package.

In Nebraska, another Trump-endorsed candidate, business executive Charles Herbster, trailed two other candidates with 24% of the projected vote tallied, according to Edison Research.

Several women have accused Herbster of sexual harassment, a charge he denies. Herbster has filed a defamation lawsuit against one of the accusers, state Senator Julie Slama. Slama has filed a countersuit alleging battery.

Trump, who also faces multiple accusations of harassment and sexual assault, said at a May 1 rally that he believed Herbster is innocent.

In early returns, Herbster trailed Jim Pillen, a hog farmer and university board member backed by the current governor.

Elsewhere in Nebraska, Republican voters in the eastern part of the state picked a nominee to succeed former Representative Jeff Fortenberry, who resigned in March after being convicted of lying to federal investigators about illegal campaign contributions.

State senator Mike Flood was projected by Edison Research to win that contest, which would put him in line for victory in November in the solidly Republican district. Flood has already won the Republican endorsement for a June 28 special election to fill Fortenberry's vacant seat through January 2023.