The Republican party has signaled plans to withdraw from traditional US presidential debates, which it claims are biased against it.

The New York Times first reported the move, citing a letter sent on Thursday by the Republican National Committee (RNC) to the Commission on Presidential Debates (CPD).

The commission was set up in 1987, as a non-partisan body “to ensure, for the benefit of the American electorate, that general election debates between or among the leading candidates for the offices of president and vice-president … are a permanent part of the electoral process”.

In the most recent election, in 2020, Donald Trump made headlines with an aggressive performance in the first debate, in Cleveland, Ohio.

The second debate was cancelled after Trump was hospitalized with Covid-19 and the CPD sought to move the event online. Trump and Republicans protested that doing so would help Joe Biden.

The final debate took place in Nashville, Tennessee as planned, with Biden widely adjudged the winner. A vice-presidential debate between Mike Pence and Kamala Harris also went ahead, in Salt Lake City.

In December this year, the Guardian first revealed the stunning news that Trump tested positive for Covid before the first debate but concealed the result, potentially putting Biden’s life in danger.

Trump said that was fake news. So did his former chief of staff Mark Meadows – who wrote the book which contained the bombshell.

The Times said the Republican move against the CPD was born of longstanding complaints that it favors Democrats, “mirroring increasing rancor from conservatives toward Washington-based institutions”.

Among Republican complaints in 2020 was that the first debate took place on 29 September, more than a month before election day but after nearly a million votes had been cast.

Trump and Republicans also complained about supposed bias among debate moderators – even from Chris Wallace, then of the conservative Fox News network, in the first debate.

Trump remains favorite to be the Republican nominee in 2024.

The threatened withdrawal from CPD debates, the Times said, followed “months of discussions between the commission and party officials”.

David Bossie, a longtime rightwing operative with strong links to Trump, was reported to be leading the RNC on the issue, seeking among other aims to insert political representatives in meetings of the CPD board.

Withdrawal will have to be approved at the RNC’s winter meetings in Utah in February, the Times said.

In her letter, according to the Times, the RNC chair, Ronna McDaniel, said: “So long as the CPD appears intent on stonewalling the meaningful reforms necessary to restore its credibility with the Republican party as a fair and nonpartisan actor, the RNC will take every step to ensure that future Republican presidential nominees are given that opportunity elsewhere.”

In a statement, the CPD said it “deals directly with candidates for president and vice-president who qualify for participation”, and said “plans for 2024 will be based on fairness, neutrality and a firm commitment to help the American public learn about the candidates and the issues”.