WASHINGTON—Former White House adviser Steve Bannon drew bipartisan ire on Capitol Hill Thursday by refusing to answer a range of questions from the House Intelligence Committee, with lawmakers vowing to take more drastic steps to compel his testimony.

Mr. Bannon, a onetime confidant of President Donald Trump who has since become estranged from him, appeared under subpoena before the committee as part of its continuing investigation into Russian interference in the 2016 U.S. presidential election.

...