Mike Pence has offered a rebuke of his one-time boss Donald Trump, saying history will hold the former president accountable for his role in the January 6 attack on the US Capitol.

Pence, then vice-president, was in the Capitol when thousands of Trump supporters breached the building in an attempt to stop Congress certifying the 2020 presidential election, which Trump lost to Joe Biden.

As Senate president, Pence presided over the ceremonial task of approving the votes of the electoral college.

Throughout the siege, Trump sent several tweets, one calling on Republicans to “fight” and others making false claims of voter fraud. He also criticised Pence for certifying the results.

Some rioters chanted “Hang Mike Pence”. A makeshift gallows was erected outside. Pence was spirited to safety by Secret Service agents.

On Saturday at the Gridiron dinner in Washington, Pence told journalists and their guests: “President Trump was wrong. I had no right to overturn the election, and his reckless words endangered my family and everyone at the Capitol that day, and I know that history will hold Donald Trump accountable.”

Pence is now considering a run for the Republican presidential nomination in 2024 – against Trump, the clear leader in polling.

Pence rarely addressed January 6 in the months after the riot but he has now upped his criticism of the rioters and Trump. In a memoir released in November he accused Trump of endangering his family.

“What happened that day was a disgrace,” Pence told the Gridiron audience. “And it mocks decency to portray it any other way. For as long as I live, I will never, ever diminish the injuries sustained, the lives lost, or the heroism of law enforcement on that tragic day.”

A Trump spokesperson did not immediately respond to a request for comment.

Pence’s remarks came a few days after the Fox News host Tucker Carlson aired highly selective, misleading security footage of the Capitol attack, in an attempt to claim many rioters were “orderly”.

Carlson’s depiction was sharply criticised by Democrats and Senate Republicans. Many other Republicans, particularly in the House of Representatives, shrugged off the episode.

On Sunday, a relatively moderate House Republican was asked if Pence was right to say history would hold Trump accountable for January 6. Nancy Mace, from South Carolina, sidestepped the question.

“I see this in two parts,” she told CNN’s State of the Union. “I think both sides are really struggling, looking at the nomination process. You’ve got some on the left that don’t want Biden to run, you’ve got those on the right that don’t want [Trump] to run.

“You know, a lot of folks on both sides keep bringing up January 6, and it’s keeping us from moving our country forward.”

Mace was not among the 10 House Republicans who voted to impeach Trump over the Capitol attack, making Trump’s second impeachment the most bipartisan in US history.

Nonetheless, she also saluted her own success in defeating a challenger endorsed by Trump last year, and said Republicans should unite behind a candidate “who can win the White House”.

Asked again if Trump would be held accountable, Mace said: “He is one of the only candidates in right now … we have a long way to go for additional candidates to jump in and see how the field lays out.”

Asked if the Republican House speaker, Kevin McCarthy, was right to have released more than 40,000 hours of Capitol security footage to Carlson – a decision for which McCarthy has faced fierce criticism – Mace said: “I said early on … it was important that it should be released to every outlet including CNN, every media outlet, every defense attorney so that the public can see for itself.

“There was violence on that day. You cannot deny that and you know, it was a dark day in our history. But so was the summer of 2020.”

Mace proceeded to compare the deadly attack on Congress – now linked to nine deaths, more than a thousand arrests and hundreds of convictions including some for seditious conspiracy – to protests for racial justice after the police murder of George Floyd in Minneapolis in May 2020.

“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.”

• Reuters contributed reporting