Democrats have questioned his impartiality over his decision to brief President Trump before members of the committee on claims that the Trump transition team had been incidentally swept up in legal surveillance from intelligence agencies. Alhough Nunes maintained that the intelligence gathering was conducted legally, it prompted Trump - who claimed his predecessor, President Barack Obama, "had my "wires tapped" in Trump Tower" - to say he felt "somewhat" vindicated.
Both Speaker of the House Paul Ryan and Nunes himself said there would be no recusal, with Nunes saying Tuesday he has "no idea" why Democrats would call for his removal from the investigation.
The Senate Intelligence Committee, which is also investigating Russia's role in the election, wants to question Trump's son-in-law and adviser, Jared Kushner, about meetings he held with the Russian ambassador and a Russian banker in December.
Nunes would not name the source of the information, and his office said he did not intend to share it with other members of the committee. Asked whether he would recuse himself, he said, "The investigation continues".
Yates, who was sacked earlier this year after refusing to implement Trump's travel ban, was notified by the Justice Department that her testimony might be problematic, The Washington Post reported. Yates herself was sacked in January after she directed Justice Department attorneys not to defend Trumps first travel ban in court.
In them, O'Neil pushes back against what he says is Justice Department guidance on what Yates could say about conversations she had with Trump - conversations the department indicated could be covered by executive privilege.
"We believe that the Department's position in this regard is overbroad, incorrect, and inconsistent with the Department's historical approach to the congressional testimony of current and former senior officials", O'Neil wrote in a March 23 letter to Justice Department official Samuel Ramer.
Mr Spicer told journalists that the White House had "encouraged" Ms Yates, who was sacked by the president for not backing his travel ban, to give evidence.
The same day she received the letter, the Chairman of the House Intelligence Committee, Congressman Devin Nunes canceled Yates' scheduled testimony.
One Republican lawmaker, Representative Walter Jones of North Carolina, went so far as to join Democrats in demanding a special committee to investigate the Russian Federation probe, telling Fox News on Tuesday that Nunes was now "tainted".
There also were demands he be bounced as chairman after he revealed he visited the White House grounds last week to review intelligence documents from a source and then relayed that information to Trump.
Associated Press writers Stephen Ohlemacher and Erica Werner contributed to this report.
"If the president puts Russian dressing on his salad tonight, somehow that's a Russian connection", White House spokesman Sean Spicer said Tuesday at his daily press briefing.