The Republican winners in Tuesday's primaries backed by Trump parrot the former president's 2020 election falsehoods, commonly known as the Big Lie, that the contest between Trump and Democratic President Joe Biden was stolen by fraud.

Among the victors, Mark Finchem won the nomination to run for Arizona's secretary of state, a position that would give him enormous sway over the conduct of elections should he prevail against his Democratic opponent in November.

Finchem attended Trump's infamous speech in Washington on January 6th, 2021, where supporters of the Big Lie rallied before marching to attack the U.S. Capitol in an failed effort to prevent Congress from certifying the results of the 2020 election.

Also in Arizona, the Associated Press reported Blake Masters secured the Republican nomination in the Senate race. Masters has Trump's endorsement and the backing of tech billionaire Peter Thiel. He's also pledged to work to impeach US President Joe Biden and prosecute Dr. Anthony Fauci, the U.S. government's top COVID-19 expert.

In Kansas, the state's Attorney General Derek Schmidt, endorsed by Trump, secured the Republican nomination for governor.

And in Michigan, Republican Representative Peter Meijer was defeated by far-right challenger John Gibbs. Meijer was one of only 10 House Republicans who voted to impeach Trump for inciting the U.S. Capitol attack.

As he flirts publicly with the possibility of running for president again, Trump has endorsed more than 200 candidates. Most are safe bets - incumbent Republicans in conservative districts - but even in competitive races many of his candidates have prevailed.

Some political analysts tell Reuters that Trump-backed candidates who support election falsehoods and downplay the violence of January 6 could imperil the Republican Party's hopes of retaking Congress in November.

A Reuters/Ipsos survey from the July found just 34% of the U.S. public views Trump favorably, compared with 60% who view him unfavorably.