"In terms of next steps I think the next steps for the Congress to take is to initiate contempt proceedings", Schiff said, adding that Bannon was given a chance to say why he should not be held in contempt.
As late as December of past year, Bannon reportedly bragged to some associates that he had not hired a lawyer and was unworried about his potential legal exposure in the multiple investigations being conducted into connections between Russian Federation and members of President Trump's campaign. He would only answer 25 questions approved by the White House. Bannon refused to answer all other questions by claiming he was invoking executive privilege on behalf of President Donald Trump.
Bannon is one of several key Trump associates whose testimony has been delayed before the House panel. He was sacked from the White House last summer, and more recently had a falling out with Trump after the January publication of a book in which he sharply criticized Trump family members.
US intelligence agencies determined more than a year ago that Moscow sought to interfere in the campaign.
Mr Bannon's attorney and White House aides did not immediately respond to requests for comment.
When Conaway was asked whether he would back such a contempt proceeding, he said the decision was not his to make.
House Intelligence Committee Chairman Rep. Devin Nunes, R-Calif., arrives for a closed-door meeting earlier this month.
"I think he should answer our questions", Conaway, who runs the panel's Russian Federation investigation, said Thursday.
At least one Republican on the intelligence panel said before the interview that a contempt vote would be necessary if Bannon were uncooperative.
Lawmakers are trying to decide whether to hold him in contempt.
"For not just our committee but every committee, that (subpoenas) don't mean anything, that it's just a hollow threat, " Rooney said. "You can't do that".
Rep. Trey Gowdy, a GOP member of House Intelligence Committee, said Thursday "I'm not OK with" Bannon refusing to answer questions about topics during the transition period.
"That's not how privilege works", Schiff said. "And we can not take that kind of stonewalling for an answer".
Rep. Mike Conaway, the Texas Republican leading the committee's Russian Federation investigation, told CNN Tuesday evening that there appears to be an agreement between the House counsel and Bannon's side for his return testimony.
Republicans were set around noon to begin their own questions. Negotiations between the House and White House have been ongoing since then, and interviews have been scheduled and postponed in recent weeks.
But Bannon's fight with the committee has drawn Democrats and Republicans together in a rare common cause, as they seek to ensure that the White House's efforts to protect Bannon do not erode the power of a congressional subpoena - something that could have "deep implications for any investigation Congress may conduct in the future", Schiff said. The interview came after Bannon met with investigators in Special Counsel Robert Mueller's probe on Monday and Wednesday, according to a person familiar with the sessions. The person declined to be named because the interview schedule isn't public.