That made Bannon the first person from Trump's inner circle to receive a grand jury subpoena from Mueller in the probe, which is also looking at whether Trump has tried to obstruct the investigation.
The House Intelligence Committee is looking into any possible coordination between the Trump campaign and Russian Federation, and is one of several groups investigating the matter.
As lawmakers probed Bannon's time working for President Donald Trump, Bannon's attorney Bill Burck was asking the White House counsel's office by phone during the Tuesday session whether his client could answer the questions.
Axios characterized the moment as a "slip-up" that stood out from the rest of Bannon's testimony, because he otherwise had declined to answer questions related to his time at the White House and during the transition.
Before the interview, which lasted much of the day, a person familiar with what the panel was planning to ask Bannon said the Intelligence Committee was trying to find out Trump's thinking when he fired FBI Director James Comey.
Schiff says that was the first time Republicans on the committee had issued a subpoena in response to a witness refusing to answer questions at the instruction of the White House.
But sitting White House officials rarely appear before the congressional panels investigating Russian Federation meddling, making Hicks' appearance even more significant - especially given her ties to the President. Attorney General Jeff Sessions made a similar case when he declined to answer some questions he had received from lawmakers in various ongoing Russian Federation probes.
China targets websites mentioning Taiwan as a country
Delta Air Lines was this week reprimanded by the Civil Aviation Administration of China for similar descriptions on its website. Media in China has reported that some travelers have cancelled reservations with Marriott as a response to the errors.
Bannon was sacked by the White House in August and returned to Breitbart News.
After Bannon's interview, Democrats on the committee accused the White House of exerting influence over Bannon to keep him from talking about his time in the West Wing, according to the New York Times.
It infuriated President Trump, who now refers to Bannon as "Sloppy Steve". In Bannon's case, however, the stonewalling was even more striking because he cited it with regard to conversations that had occurred either during the transition period or after Bannon had left the White House, both of which would not normally be covered by executive privilege.
Bannon, his attorney and his spokeswoman did not respond to requests for comment.
"As with all congressional inquiries touching upon the White House, Congress must consult with the White House prior to obtaining confidential material", Sanders said. Bannon's refusal to answer committee questions followed a subpoena issued by chair Devin Nunes (R-CA) in the middle of Bannon's testimony.
In Michael Wolff's "Fire and Fury", Bannon accuses Donald Trump Jr., Jared Kushner and former Trump campaign chairman Paul Manafort of essentially betraying the nation by meeting with a group of Russian lawyers and lobbyists who they believed were ready to offer "dirt" on Democratic candidate Hillary Clinton. It could also signal that Mueller is seeking to pressure Bannon to agree to an interview with his investigators.
Mr Bannon, a champion of the President's "America First" agenda, was among Mr Trump's closest aides during the 2016 campaign, the presidential transition and his first few months in office.
Some legal experts said the subpoena could be a sign that the investigation was intensifying, while others said it might simply have been a negotiating tactic to persuade Bannon to cooperate with the investigation.