The family of Brian Sicknick, the US Capitol police officer who died the day after the January 6 attack on Congress, condemned Tucker Carlson and Fox News as “unscrupulous and outright sleazy”, after the primetime host made first use of security footage from the riot bestowed by Kevin McCarthy, the Republican House speaker.

A statement on Tuesday said: “The Sicknick family is outraged at the ongoing attack on our family by the unscrupulous and outright sleazy so-called news network of Fox News.”

Fox and Carlson, the family said, “will do the bidding of [Donald] Trump or any of his sycophant followers, no matter what damage is done to the families of the fallen, the officers who put their lives on the line and all who suffered on January 6, due to the lie started by Trump and spread by sleaze-slinging outlets like Fox”.

Nine deaths have been linked to the attack on the Capitol by supporters Trump told to “fight like hell” in service of his lie that his defeat by Joe Biden was the result of electoral fraud.

Trump aimed to stop certification of Biden’s win. The process was only delayed but lawmakers including the vice-president, Mike Pence, were sent running for their lives.

More than 1,000 people have been charged and hundreds convicted on charges including seditious conspiracy. Hundreds remain wanted by authorities.

Trump was impeached for inciting the attack but acquitted when enough Senate Republicans stayed loyal. The House January 6 committee made four criminal referrals regarding Trump to the Department of Justice.

Last month, to protests from Democrats and media groups, McCarthy made 41,000 hours of security footage available to Carlson and Fox News.

Carlson had already claimed January 6 was a “false flag” attack, staged by authorities to entrap Trump supporters. On Monday night, he tried to portray those who stormed the Capitol as peaceful protesters.

Saying the tapes showed “mostly peaceful chaos”, Carlson said: “Taken as a whole the video record does not support the claim that January 6 was an insurrection. In fact, it demolishes that claim.”

In return, the Sicknick family lambasted Carlson and Fox News.

Fox News, they said, “has shown time and time again that [it is] little more than the propaganda arm of the Republican party, and like Pravda will do whatever [it is] told to keep the hatred and the lies flowing while suppressing anything resembling the truth.

“Fox does this not for any sense of morality as they have none but for the quest for every penny of advertising money they can get from those who buy airtime from them.”

Recent revelations from filings in a $1.6n defamation suit from Dominion Voter Systems include Rupert Murdoch, Fox News’ owner, indicating he knew Trump’s claims were false but saying his motivation for accommodating election deniers was to stop viewers deserting.

The Sicknick family also called McCarthy a “disgusting excuse for a House speaker”. Later on Tuesday, the Republican leader in the Senate, Mitch McConnell, was asked if McCarthy had made a mistake in giving Carlson the tapes.

He said: “My concern is how [the riot] was depicted, which was a different issue. Clearly the chief of the Capitol police, in my view, correctly describes what most of us witnessed first-hand on January 6.”

McConnell’s Democratic counterpart, Chuck Schumer, lamented “one of the most shameful hours we have ever seen on cable television” and said Carlson had shown “contempt for the facts [and] disregard of the risks [while] knowing full well he was lying to his audience”.

Carlson, Schumer said, “told the bald-faced lie that the Capitol attack, which we all saw with our own eyes, somehow was not an attack at all”.

Decrying efforts to make a martyr out of Ashley Babbitt, a Trump supporter shot dead by a police officer on January 6, the Sicknick family said Carlson was “downplaying the horrid situation faced by US Capitol police and DC Metro police who were incredibly outnumbered and were literally fighting for their very lives”.

Sicknick, 42, was sprayed with chemicals, for which his attacker was jailed for nearly seven years. Sicknick died the day after the riot, after suffering two strokes. A medical examiner said he died of natural causes but his name remains linked to January 6. His body lay in state at the Capitol.

Sicknick’s family said “his sense of duty and incredible work ethic were the driving force which sent him back in spite of his injuries and no doubt contributed to his succumbing to his injuries the following day.

“What will it take to silence the lies from people like Carlson? What will it take to convince people that the January 6 insurrection was very real, it was very violent, and that the event was orchestrated by a man [Trump] who is every bit as corrupt and evil as Vladimir Putin.

“The Sicknick family would love nothing more than to have Brian back with us and to resume our normal lives. Fictitious news outlets like Fox and its rabid followers will not allow that. Every time the pain of that day seems to have ebbed a bit organisations like Fox rip our wounds wide open again and we are frankly sick of it.

“Leave us the hell alone and instead of spreading more lies from Supreme Leader Trump, why don’t you focus on real news?”

Fox News did not comment.