Former Donald Trump advisor Steve Bannon Tuesday refused to answer questions from a congressional committee probing the president's campaign links to Russia, saying he was under orders from the White House not to.

Bannon was quizzed voluntarily behind closed doors by the House of Representatives Intelligence Committee, the first time he has testified in the probe investigating whether Trump's campaign colluded with Russia in its bid to influence the 2016 US elections.

It was unlikely to be Bannon's last such testimony: the New York Times and the Washington Post reported late Tuesday that Bannon has been subpoenaed by Robert Mueller, the Justice Department special counsel investigating the same issue.

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.

When appearing before the Intelligence Committee, Bannon refused to answer a number of questions, citing "executive privilege" allowing the president to keep information from the public.