Nunes, who was a member of the Trump transition team, came under fire for meeting a source on White House grounds the day before he delivered an unexpected briefing to President Trump about his concerns about the "incidental" collection and potential "unmasking" of Americans within the intelligence community.
Nunes also drew criticism for briefing the president ahead of his committee and said he would not divulge to his colleagues the sources of his information.
Pressed on whether he's considering stepping down from the House investigation, Nunes said he has "no idea" why Democrats want him to remove himself from the House's sensitive investigation.
"I'd like to know, first, what the purpose of [a recusal] would be. Why that would be?" he said. "Because someone asks? I mean that's not how ... decisions are made."
Nunes stressed that no Republicans have echoed the Democrats' calls for a recusal, a statement that was accurate at the time he made it.
"My colleagues are perfectly fine. I mean, they know we're doing an investigation, and that will continue," he said. "We're doing a very thorough job on this investigation. As you know, this Russia issue, we have been on it for many, many years, and so we'll continue to be on the issue."
Later in the day Tuesday, Rep. Walter Jones, R-N.C., became the first member of the GOP to say Nunes should recuse himself. Jones has a reputation for deviating from his party and is not a member of the Intelligence Committee.
Asked whether the investigation will continue with him as chairman, Nunes replied, "Why would it not?"
At today's White House press briefing, press secretary Sean Spicer would not comment on what the administration believes Nunes should do.
"That is entirely up to the speaker and the House of Representatives," he said.