The conservative Republican Liz Cheney and the chief executive of the Anti-Defamation League led condemnation of Fox News and Tucker Carlson, after the primetime host announced a series about the supposed “true story” of the deadly attack on the US Capitol on 6 January.

They denounced Carlson for spreading dangerous conspiracy theories in the latest scandal to engulf a man whose popularity belies his record of racist and untrue statements on issues from immigration to racial justice.

“Fox News is giving Tucker Carlson a platform to spread the same type of lies that provoked violence on 6 January,” tweeted Cheney, a Wyoming representative on the dwindling anti-Trump wing of the Republican party.

Jonathan Greenblatt, of the ADL, wrote to Lachlan Murdoch, chief executive of Fox Corporation, to demand the series be shelved.

“Clearly Carlson has the right to make outrageous claims,” Greenblatt wrote. “But freedom of speech is not freedom of reach. You have no obligation to validate his views with airtime on your platform and, I would argue, a moral responsibility not to do so.”

Greenblatt has previously called for Carlson to be fired over his advocacy of the racist replacement theory, which says Democrats encourage immigration to keep Republicans out of power. Lachlan Murdoch rejected that request.

In the trailer for Carlson’s series, Patriot Purge, a pundit says: “False flags have happened in this country, one of which may have been 6 January.”

Among conspiracy theorists, “false flag” events are said to be staged by the government to pursue nefarious ends. Some claim the 9/11 terrorist attacks were false flags. The InfoWars host Alex Jones, a Trump ally and supporter, has landed in legal and financial jeopardy after claiming the Sandy Hook school shooting of 2012, in which 20 young children and six adults were killed, was a false flag attack.

Carlson has called the 6 January riot “a political protest that got out of hand”. He has also claimed it was organised by the FBI.

Cheney said: “As Fox News knows, the election wasn’t stolen and 6 January was not a ‘false flag’ operation.”

Five people including a Trump supporter shot by law enforcement and a police officer died around the Capitol attack. The riot followed a “Stop the Steal” rally near the White House at which Trump told supporters to march on Congress and “fight like hell” to overturn the election.

Trump was impeached for inciting an insurrection. Cheney was one of 10 House Republicans who voted to send him to the Senate for trial but only seven Republican senators joined Democrats in finding Trump guilty and he was not convicted. He is free to run for office again, fundraising strongly and dominating polls regarding possible candidates for 2024.

Trump has stuck to his lie that the election was stolen, a claim rejected by his own attorney general, Republican officials in key states and a succession of judges. The Republican party has swung behind Trump, also seeking to play down the events of 6 January, a day which has led to more than 600 arrests.

Another outlet owned by Rupert Murdoch, the Wall Street Journal, was condemned this week for printing a letter in which Trump repeated his election lies.

In another tweet, Cheney asked Carlson: “Are you still falsely contending the voting machines were corrupted and the election was stolen?” She included the Twitter handles of Rupert Murdoch, Fox News’s chief executive, Suzanne Scott, its president and executive editor, Jay Wallace, and the former House speaker Paul Ryan, now a member of the Fox board. None commented.

Fox News did not respond to a request for comment.

On Thursday another Fox News personality, Geraldo Rivera, told the New York Times Carlson was “wonderful” and “provocative” but said things that were “inflammatory and outrageous and uncorroborated”. On Twitter, Rivera called the “false flag” claim in Carlson’s trailer “bullshit”.

Carlson’s series will premiere on the Fox Nation streaming service on Monday. Scored to martial drums, its trailer says it will tell the “the true story behind 1/6 … the war on terror 2.0 and the plot against the people”.

“The domestic war on terror is here and it’s coming after half of the country,” a pundit says, over shots of helicopters near the Capitol and the title, Patriot Purge.

Carlson says: “The helicopters have left Afghanistan and now they’ve landed here at home.”

On Thursday, Carlson claimed: “What we found … bore no resemblance whatsoever to the story that you have heard repeatedly from Liz Cheney and Nancy Pelosi, as well as their many obedient mouthpieces in the media. They were lying.”

In his trailer, another pundit says: “The left is hunting the right, sticking them in Guantánamo Bay for American citizens, leaving them to rot.”

The trailer also splices footage of Trump speaking with a shot of Osama bin Laden, while scenes outside the Capitol on 6 January are scored to the Battle Hymn of the Republic. The trailer culminates with the refrain of that civil war song: “The truth is marching on.”

In his letter to Rupert Murdoch, Greenblatt of the ADL wrote: “Let’s call this what it is: an abject, indisputable lie and a blatant attempt to rewrite history.”