Geraldo Rivera criticizes his Fox News colleague Tucker Carlson.

Tucker Carlson, the top-rated Fox News host, faced criticism on Thursday — including from a prominent colleague at his own network — after he announced plans for a documentary series featuring debunked conspiracy theories about the Jan. 6 riot at the United States Capitol.

The three-part series, “Patriot Purge,” is set to be broadcast next month on Fox News’s streaming service, Fox Nation. An 84-second trailer that aired on Fox News on Wednesday included the baseless suggestion that the riot was a so-called “false flag” operation created to demonize the political right.

As tense music plays on the soundtrack, Mr. Carlson says in ominous tones that “the helicopters have left Afghanistan and now they’ve landed here at home.” Various speakers convey the false idea that Democrats want to persecute and imprison conservatives.

The trailer evoked a dismayed public response from Geraldo Rivera, the veteran Fox News correspondent, who used a profane term in a Twitter post to dismiss the claim that the Capitol riot was a “false flag” operation. That theory has repeatedly been debunked.

Speaking on Thursday with The New York Times, Mr. Rivera elaborated on his concerns.

“Tucker’s wonderful, he’s provocative, he’s original, but — man oh man,” Mr. Rivera said in a phone interview. “There are some things that you say that are more inflammatory and outrageous and uncorroborated. And I worry that — and I’m probably going to get in trouble for this — but I’m wondering how much is done to provoke, rather than illuminate.”

“Messing around with Jan. 6 stuff … ” Mr. Rivera added, pausing briefly. “The record to me is pretty damn clear, that there was a riot that was incited and encouraged and unleashed by Donald Trump.”

Asked if he would urge his Fox News bosses to reconsider airing Mr. Carlson’s special, Mr. Rivera demurred, saying, “I don’t want to go there, that’s not my job.”

But he added of Mr. Carlson: “He’s my colleague. He’s my family. Sometimes you have to speak out about your family.”

Fox News did not immediately respond to a request for comment.

Mr. Carlson’s prime-time provocations have helped propel him to the highest ratings in cable news, even as he has used rhetoric sometimes used by white nationalists. He has frequently questioned the coverage of the Jan. 6 attack, asserting that government agents were involved in the events and portraying the rioters as mostly peaceful.

“The vast majority of people inside the Capitol on Jan. 6 were peaceful,” he told viewers on Sept. 23. “They were not insurrectionists, they shouldn’t have been there. They weren’t trying to overthrow the government. That’s a total crock.”

The trailer for “Patriot Purge” includes an interview with Darren Beattie, a former speechwriter in the Trump White House who was fired in 2018 after it was revealed that he had attended a gathering with white nationalists. Ali Alexander, a far-right activist and one of the most prominent advocates of the falsehood that President Biden stole the 2020 election, also appears in the trailer.

Among Mr. Carlson’s critics on Thursday was Representative Liz Cheney, a Wyoming Republican. In a Twitter post, she accused Fox News of giving Mr. Carlson “a platform to spread the same type of lies that provoked violence on January 6.”

Mr. Rivera, who is scheduled to appear on Thursday’s episode of the Fox News afternoon program “The Five,” recently renewed his contract with the network in a multiyear deal. In an announcement last month, Suzanne Scott, the chief executive of Fox News Media, described Mr. Rivera as “an important voice on Fox News Channel over the last two decades,” adding, “We are thrilled to have him continue to be a part of the Fox family.”

Fox News was not the only arm of Rupert Murdoch’s media empire facing scrutiny this week. The Wall Street Journal was criticized on Wednesday for publishing a lengthy letter to the editor from former President Donald J. Trump that contained numerous falsehoods about the integrity of the 2020 election.

Davey Alba contributed reporting.