Bannon was not planning on showing up ahead of a Tuesday deadline because the White House and committee haven't reached an agreement over the scope of the questioning, a source said Monday.
Schiff said this "ban" on Bannon's testimony covered issues between Trump's election and inauguration, his time at the White House and communications with Trump since, even though Trump has not invoked executive privilege.
The house panel wants Mr Bannon to testify as part of its investigation of allegations that Russian Federation sought to influence the 2016 presidential election in the United States, following up on his January 16 appearance that failed to satisfy some members of the committee.
Among the options available if Bannon continues to refuse to comply with the committee's subpoena is a contempt finding against him.
Mr. Bannon is reportedly cooperating with the Mueller probe and will be interviewed by the special counsel's team next week, according to a CNBC report Tuesday. This is the third time the committee has had to delay Bannon's testimony after his initial appearance last month.
Bannon declined to answer the questions in light of executive privilege concerns, a claim of privilege Rep. Adam Schiff, the panel's top Democrat, called "breathtaking".
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Committee members from both parties have denounced the White House's prohibitions, and stated that they could hold Bannon in contempt of Congress.
Conway's office said the committee itself - which is investigating Russian interference in the 2016 election - had chose to delay the interview with Bannon. According to one of the sources speaking with Reuters, Bannon would answer Mueller's questions when he appears to testify before him. That meeting took place between members of Trump's campaign team and a Russian lawyer who had promised Donald Trump, Jr. compromising information on 2016 Democratic nominee Hillary Clinton.
Things haven't gone Steve Bannon's way since he got on the wrong side of President Trump.
The White House did not immediately respond to a request for comment and neither did an attorney for Bannon.
"But again, I expect him to be here, expect him to answer the questions, and [we'll] go from there", Conaway said.