Representative Bennie Thompson, a Democrat, said on NBC's "Meet The Press" that the committee is examining whether it can lawfully issue subpoenas to sitting members of Congress.
"I think there are some questions of whether we have the authority to do it," Thompson said. "We're looking at it. If the authorities are there, there'll be no reluctance on our part."
Thompson chairs the House of Representatives Select Committee on Jan. 6, which is expected to hold public hearings and issue reports in the coming months.
The committee is trying to establish then-President Donald Trump's actions while thousands of his supporters attacked police, vandalized the Capitol and sent members of Congress and then-Vice President Mike Pence running for their lives. Congress had been meeting to count the electoral votes that gave Democrat Joe Biden victory in the November 2020 presidential election.
Multiple people close to Trump, including conservative media TV hosts, urged him during the riot to make a televised speech telling his supporters to stop the attack. Trump waited hours before releasing a prerecorded message.
Representative Liz Cheney, the panel's Republican vice chair and a harsh critic of Trump, told ABC News he had committed "dereliction of duty" on Jan. 6 and the panel should consider "enhanced penalties" for that kind of action. The American people, she said, need to understand "how dangerous Donald Trump was."
The committee sent a letter on Dec. 22 to Representative Jim Jordan, a Republican and ardent Trump ally, asking for testimony about his telephone conversations with Trump on Jan. 6.
Jordan said in a recent Fox News interview that he had "real concerns" about the committee's credibility, but was reviewing its letter to him.
The request came two days after a similar letter to Republican Representative Scott Perry.
The committee requested Perry's testimony about Trump's attempts to oust Jeffrey Rosen, who was acting head of the U.S. Justice Department during the closing weeks of his presidency, and replace him with Jeffrey Clark, an official who at the time was trying to help Trump overturn his election defeat.
Perry declined to cooperate, posting on Twitter on Dec. 21 that the committee "is illegitimate, and not duly constituted."
An appeals court ruled earlier last month that the committee was legitimate and entitled to see White House records Trump has tried to shield from public view.