Adam Kinzinger, one of two Republicans on the House committee investigating the deadly 6 January Capitol attack incited by Donald Trump, said on Sunday he was not “yet” ready to declare the former president guilty of a crime – but that the panel was investigating the likelihood that he is.

“Nobody is above the law,” the Illinois congressman told CNN’s State of the Union. “And if the president knowingly allowed what happened on 6 January to happen, and, in fact, was giddy about it, and that violates a criminal statute, he needs to be held accountable for that.”

The committee has been picking up pace in recent weeks with dozens of subpoenas issued, some to close Trump aides. The waters lapped at the doors of Trump’s Oval Office this week when his fourth and final chief of staff, Mark Meadows, became a focus of the investigation over tweets he received on and around the day of the insurrection.

The committee voted unanimously to refer Meadows for criminal prosecution for contempt of Congress, after he withdrew his cooperation.

Kinzinger, who alongside fellow Republican Liz Cheney has drawn the ire of Trump allies for serving on the committee, said he had no qualms about scrutinising how Trump incited supporters to try to overturn his election defeat by Joe Biden, which he says was the result of massive electoral fraud, which it was not.

“He’s not a king,” Kinzinger said, “Former presidents, they aren’t former kings.”

Kinzinger added that he feared the events of 6 January were “trial run” for Trump and his allies to attempt another coup.

“We will get every bit of detail that we can possibly get on that, so that’s important for the president’s role,” he said. “I want to hold the people guilty accountable but I want to make sure this never happens again.

“Otherwise, 6 January will have been, yes, a failed trial run, but, sometimes, a failed trial run is the best practice to get one that succeeds, a coup that would succeed in toppling our government.”

Kinzinger’s comments are the strongest to date about the depth of the inquiry into Trump’s role.

At a “Stop the Steal” rally near the White House on 6 January, the then-president urged supporters to march on the Capitol and “fight like hell [or] you’re not going to have a country any more”.

He was impeached a second time for inciting the insurrection that followed, but though Kinzinger, and nine other House Republicans and seven GOP senators voted with Democrats, Trump was acquitted in his Senate trial and remains free to run for office again.

Pressed on whether he thought Trump was guilty of a crime, Kinzinger said: “I don’t want to go there yet, to say, ‘Do I believe he has’. But I sure tell you I have a lot of questions about what the president was up to.”

Earlier this month at a sentencing hearing for one of the rioters, a district court judge, Amy Berman Jackson, said she believed Trump stoked the riot and should be held accountable. Jackson was one of a growing number of federal judges to speak out.

Trump is also in legal jeopardy from investigations of his business affairs, with authorities in New York looking at tax issues in particular.

Trump spoke to Fox News’s Sunday Morning Futures but was not asked about the 6 January inquiry, instead riffing on subjects including the Taliban’s hatred of dogs and how Biden’s chief medical adviser, Dr Anthony Fauci, struggles to pitch a baseball.

Trump also weighed in on a conspiracy theory popular on Fox News which says Biden is not running the country, based on an apparent gaffe in which he called his vice-president, Kamala Harris, “president” in a university commencement speech this week.

On CNN, Kinzinger acknowledged the 6 January committee was working to complete its work before next year’s midterm elections, in which Republicans are likely to take back control and thereby kill the investigation.

The Ohio congressman Jim Jordan, a Trump loyalist whose text messages were included in those released this week, was one of the Republicans rejected by the House speaker, Nancy Pelosi, for a place on the 6 January panel.

Regardless, Jordan has been tipped as a possible judiciary committee chair – who would therefore act to close the investigation of the Capitol attack.

“He could not credibly head the [judiciary] committee,” Kinzinger said. “But he certainly could head the committee.”