In an apparent swipe at the Fox News host Tucker Carlson, the anti-Trump Republican Liz Cheney said on Sunday it was “dangerous” and “un-American” to suggest the deadly assault on the US Capitol on 6 January was a “false flag” attack.

Conspiracy theorists say “false flag” attacks are staged by the government to achieve its own ends. A documentary produced by Carlson for the Fox Nation streaming service, Patriot Purge, contains such a suggestion about the Capitol attack.

Five people died around the events of 6 January, when Trump supporters stormed the Capitol in an attempt to overturn his election defeat by Joe Biden.

Trump was impeached for inciting the attack but escaped conviction when sufficient Republican senators stayed loyal.

Cheney, who has condemned Carlson’s series before, spoke to Fox News Sunday. The host, Chris Wallace, asked if there was “any truth” to claims 6 January was “a false flag operation, a case of liberals in the deep state setting up conservatives and Trump supporters”.

Cheney replied: “None at all. It’s the same thing that you hear people saying 9/11 is an inside job. It’s un-American to be spreading those kinds of lies, and they are lies.”

Cheney, who voted to impeach Trump, is one of two Republican members of the House select committee investigating the Capitol attack. The other, Adam Kinzinger of Illinois, will retire from the House next year.

But the Wyoming congresswoman, a stringent conservative whose father is the former vice-president Dick Cheney, has shown no sign of yielding despite losing her leadership position in Washington and attracting a primary challenger back home.

Cheney appeared on Sunday with the South Carolina congressman Jim Clyburn, the Democratic chief whip, with whom (and Wallace) she was this weekend honoured for being willing to work across the aisle.

“We have an obligation that goes beyond partisanship,” Cheney said, “Democrats and Republicans together, to make sure that we understand every single piece of the facts about what happened [on 6 January] and to make sure that people who did it are held accountable.

“And to call it a false flag operation to spread those kinds of lies is really dangerous.”