The Republican speaker of the US House, Kevin McCarthy, said on Sunday he would “slowly roll out” to networks other than Fox News more than 40,000 hours of security footage from the January 6 attack on Congress.

“We will slowly roll out to every individual news agency,” McCarthy told Sunday Morning Futures, a show broadcast by Fox News. “They can come see the tapes as well. Let everyone see them to bring their own judgment.”

McCarthy has only let Fox News see the tapes so far, giving access to the primetime host Tucker Carlson.

The move was blasted by Democrats in Congress and Republican critics of Donald Trump – who incited the Capitol attack in an attempt to overturn his election defeat – even before Carlson showed his first excerpts this week.

Carlson claimed the tapes showed “mostly peaceful chaos”, Trump supporters acting like tourists, and that many of more than 1,000 people arrested, some convicted of crimes including seditious conspiracy, had been unjustly targeted.

Carlson continued to show the footage even as filings in a $1.6bn defamation lawsuit against Fox News by a voting machine company showed that in private messages, Fox News hosts said Trump was lying about voter fraud in the 2020 election and Carlson himself professed to “passionately hate” the former president.

On Sunday, McCarthy claimed he did not “give” the tapes to Carlson.

“I didn’t give the tapes,” he said. “I allowed [him] to come see them, just like an exclusive with anybody else. My goal here is transparency.”

McCarthy also wielded a common rightwing talking point, likening January 6 – a violent assault linked to nine deaths including law enforcement suicides – to protests for racial justice after the police murder of George Floyd in summer 2020 which sometimes turned violent.

McCarthy said: “Why did I watch federal courts, why did I watch cities burn, federal agencies or something, and nobody arrested there? I think we should have equal justice across this country.”

Nancy Mace, a relatively moderate Republican from South Carolina, tried to make the same point on CNN’s State of the Union.

Though she said the tapes should have been given to “every media outlet”, Mace added: “We saw very few arrests when there were attacks by … members of Antifa and Black Lives Matter. I had my house spray-painted two summers ago and no one’s been held to account for that.”

Mace was not pressed by her host. But other Republicans spoke unfavourably of McCarthy’s decision to give the Capitol tapes to Carlson, and how Carlson used them.

At a Washington dinner on Saturday night, former vice-president Mike Pence, who the mob targeted on January 6, said: “Make no mistake about it, what happened that day was a disgrace. And it mocks decency to portray it any other way.”

On Sunday, speaking to CBS’s Face the Nation, Michael McCaul, the Republican chair of the House homeland security committee, said: “I think the American people deserve to see all the footage from that day, and all the footage is not going to be, you know, tourism at the Capitol.

“It’s going to show a very dark, tragic day that I witnessed firsthand, that included our Capitol police being assaulted, 140 of them injured, two pipe bombs. One Capitol police officer killed, and a protester killed. That’s not a good day.”