The White House did not tell former chief strategist Stephen Bannon to invoke executive privilege and refuse to answer questions in Congress's Russia investigation, President Trump's top aide said Wednesday.

"No," White House chief of staff John Kelly said on Fox News when asked if Bannon was instructed to assert executive privilege.

"Steve has had very, very little contact with the White House since he left," Kelly said, with the "exception of a few phone calls."

The comments appeared to counter claims by Rep. Adam Schiff (Calif.), the top Democrat on the House Intelligence Committee, that the White House imposed a "gag order" on Bannon during his testimony before the panel this week.

Bannon angered lawmakers on the committee by refusing to answer questions related to his time in the White House and the presidential transition.

Schiff told reporters Tuesday that Bannon's counsel conferred with the White House after the committee issued a subpoena to force him to testify and Bannon "was instructed by the White House to refuse again to answer any questions concerning the time during the transition and his time in the administration."

Bannon's appearance was voluntary and he did not formally invoke any form of executive privilege, which as a non-administration official, Rep. Mike Conaway (R-Texas) said, he would not be able to do.

"This witness is not an executive," Conaway, who is spearheading the committee's Russia investigation after Chairman Devin Nunes (R-Calif.) recused himself last year, told reporters Tuesday. "He's not in a position to be able to do that."

But lawmakers from both parties nevertheless characterized the limits Bannon tried to place as a form of executive privilege.

Rep. Jim Himes (D-Conn.) a member of the panel, said Bannon used a "remarkably broad definition of executive privilege" to avoid questions about his service in the administration.

"So while we were able to ask and answer a lot of different kinds of questions, there were an awful lot of questions we weren't able to answer based on this very novel theory of executive privilege," Himes said on CNN.

White House press secretary Sarah Huckabee Sanders told reporters officials are "following the same practice that many White Houses before us have that have gone back decades" with regard to congressional testimony.

"Any time you have congressional inquiries touching upon the White House, the Congress should consult with the White House prior to obtaining confidential material. This is part of a judicial-recognized process. We want to follow through that," Sanders said.

The spokesman said the White House has been "fully cooperative with the ongoing investigations."

- Katie Bo Williams contributed

Updated: 7:05 p.m.