Donald Trump cannot hide behind immunity from criminal prosecution and faces the possibility of being debarred from running for public office over his role in the Capitol attack, several members of Congress said on Sunday.

Days after the anniversary of the 6 January insurrection that left five people dead and scores injured after Trump supporters attempted to scupper the certification of Joe Biden’s victory in the 2020 election, the threat of possible criminal proceedings looms large over the former president.

Lawmakers from both main parties, including moderate Republicans, warned on Sunday that Trump will not be spared criminal liability should evidence emerge that he actively coordinated the attack.

A Republican senator, Mike Rounds from South Dakota, told ABC’s This Week that any immunity from prosecution that Trump enjoyed while in the White House evaporated on 20 January 2021, when he left office.

“The shield of the presidency does not exist for someone who was a former president – everybody in this country is subject to the courts of this country,” Rounds said.

Rounds added that it was up to the justice department, not Congress, to decide whether evidence existed of criminal wrongdoing by Trump.

On Saturday, the Guardian revealed that the House select committee investigating 6 January is homing in on the question of whether Trump led a criminal conspiracy to try and block Biden’s certification as his successor in the White House.

Depending on what they find, the committee has the power to refer the matter to the Department of Justice for possible criminal prosecution.

Adam Kinzinger, a Republican congressman from Illinois who sits on the committee, underlined the laser-like focus of the investigation on Trump’s potential complicity.

Speaking on NBC’s Meet the Press, he said the key question now was: “What did the president know about 6 January leading up to 6 January?”

Kinzinger added that the panel wanted to know why Trump failed to take any action for almost three hours while the violence at the Capitol was unfolding on his TV screen. Was it a sign of weakness or complicity?

“It’s the difference between, was the president absolutely incompetent or a coward on 6 January when he didn’t do anything or did he know what was coming? That’s a difference between incompetence with your oath and possibly criminal.”

While the question of whether the former president broke the law is fast rising up the political agenda, Congress is also considering another potential route to hold Trump accountable for the violence of a year ago: action under the 14th amendment of the constitution.

Section three of the amendment holds that nobody in elected federal office, including the president, should engage in “insurrection or rebellion” against the union.

Jamie Raskin, a Democrat from Maryland who led the second impeachment of Trump for “incitement of insurrection”, told ABC the 14th amendment might yet be “a blockade for [Trump] ever being able to run for office again”.

While the relatively tiny number of moderate Republicans who have been willing openly to criticize the former president were airing their views on Sunday, the opposing tack taken by most party leaders was also on display.

Senator Lindsey Graham, a Trump loyalist from South Carolina, told a New York radio channel the Capitol attack was a “dark day”, but went on to lambast Biden for marking the anniversary this week.

“It was an effort on his part to create a brazen political moment to try to deflect from their failed presidency,” Graham said.

A moment of silence staged at the House to mark the anniversary was attended by only two Republicans: the congresswoman Liz Cheney and her father, the former vice-president Dick Cheney.

Afterwards, the older Cheney expressed his disappointment at the “failure of many members of my party to recognize the grave nature of the 6 January attacks and the ongoing threat to our nation”.

Asa Hutchinson, the Republican governor of Arkansas, attempted to defend congress members from his state, all of whom sat out the anniversary proceedings.

“I don’t know that absolute attendance was the only way to show frustration with 6 January,” he told CNN’s State of the Union.

But Hutchinson did say he regretted that large numbers of Republican candidates running for public office are openly embracing Trump’s big lie that the 2020 election was rigged.

“What worries me is that they are not demonstrating leadership,” he said.

“We have to make clear that [6 January] was unacceptable, it was an attempt to stop the peaceful transfer of power and we have to make clear that President Trump had some responsibility for that.”