Criminal charges are possible for more associates of Donald Trump refusing to cooperate with the House committee investigating the 6 January Capitol attack, a senior Democrat warned on Sunday, two days after the indictment of former White House adviser Steve Bannon.

Adam Schiff, chair of the House intelligence committee and a member of the panel investigating the deadly Capitol riot, also said some witnesses could be offered immunity in exchange for testimony in order to advance the inquiry.

He told NBC’s Meet the Press he believed “without a doubt” that the justice department decision to charge Bannon with contempt of Congress would “shake loose” defiant Trump associates.

That could include the former chief of staff Mark Meadows, who did not show up for a deposition before the select committee on Friday, shortly before Bannon’s indictment was announced.

“Now that witnesses see that if they don’t cooperate, if they don’t fulfill their lawful duty when subpoenaed, that they too may be prosecuted, it will have a very strong focusing effect on their decision making,” Schiff said.

“Even before the justice department acted, it influenced other witnesses who were not going to be Steve Bannon.

“When ultimately witnesses decide, as Meadows has, that they’re not even going to bother showing up, that they have that much contempt for the law, then it pretty much forces our hand and we’ll move quickly.”

Schiff would not be drawn on whether that meant the committee would issue a criminal contempt referral for Meadows, who, unlike Bannon, was a government employee on 6 January. But he said the panel would decide quickly, and that it wanted to make sure “we have the strongest possible case to present to the justice department, and for the justice department to present to a grand jury”.

Meadows’ lawyer has said his client will not appear before the committee unless compelled to do so by a judge.

Schiff conceded that certain witnesses, whom he did not identify, could receive limited immunity instead of criminal referral in exchange for their cooperation, the decisions to be made on a case by case basis.

“With certain specific witnesses, we ought to consider it,” he said. “But as that kind of immunity makes it very difficult to prosecute not just them, but sometimes others, we need to think about it very carefully.”

Schiff said he saw the developments “as an early test of whether our democracy was recovering” from the turmoil of the Trump administration.

“Basically … the Republican party, at the top levels, that is Donald Trump and those around him, seem to feel that they’re above the law and free to thwart it. And there’s something admirable about thumbing your nose at the institutions of our government.

“Bannon did what he did because for four years that’s what worked. They could hold Republican party conventions on the White House grounds. They could fire inspectors general, they could retaliate against whistleblowers. It was essentially a lawless presidency and they were proud of it. That ought to concern every American. We need a reestablishment of the rule of law in this country and I’m glad to see that that’s happening.”

Bannon’s indictment, and the threat of charges for Meadows, marked a significant escalation in the House committee’s efforts to get to the bottom of the 6 January riot and Trump’s attempt to overturn defeat by Joe Biden.

Trump himself is locked in legal battle with the committee over the release of White House documents related to the day of the insurrection, when his supporters ransacked the Capitol.

On Thursday, a federal appeals court in Washington DC handed Trump a temporary victory by blocking the release by the National Archives of hundreds of pages of communication logs, memos and other materials ordered by a lower court days before. The appeals court will listen to arguments later this month on Trump’s claim the documents are protected by executive privilege before making a final decision.

Schiff said he believed efforts to delay the inquiry in the courts would not succeed.

“The courts themselves have recognised that Donald Trump essentially played our institutions for four years and played rope-a-dope in the courts,” he said.

“[They] moved with such expedition to reject Trump’s claims in the district court a week or so ago, now the court of appeals is saying they’re going to have a hearing by the end of the month. Courts don’t generally move that fast and I think it’s a recognition that Donald Trump has relied on justice delayed meaning justice denied. So we and the courts are moving quickly.”