The White House believed that it had reached an agreement with the House Intelligence Committee that would limit the scope of the panel's questions for Stephen Bannon solely to his time on Trump's presidential campaign, a White House official told CNBC.

The official said the White House had met with staffers on the Intelligence panel ahead of Bannon's interview and determined that the committee would not ask Bannon about his time on Trump's presidential transition team or in the White House. Bannon served for a period as Trump's chief strategist in the White House.

But when Bannon's lawyer informed the White House during his interview Tuesday that the panel was asking about issues related to the former chief strategist's time in the White House and on the transition team, he was instructed to decline answering those questions.

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"We said 'Hey, hey, pump the brakes,' " the official told CNBC. "We said to Bannon, 'Don't answer those questions because we haven't agreed to that scope under the process.' "

Lawmakers from both parties were frustrated on Tuesday by Bannon's refusal to answer questions about his time in the White House or on the transition team, and Rep. Adam Schiff Adam Bennett SchiffTop Democrats call for DOJ watchdog to probe Barr over possible 2020 election influence Overnight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Overnight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies MORE (Calif.), the panel's top Democrat, accused the White House of issuing a "gag order" on Bannon.

The Associated Press reported Wednesday that Bannon's lawyer relayed questions to the White House, during his client's appearance before the committee, to check whether Bannon could answer certain questions.

The committee is looking into Russian meddling in the 2016 presidential election and whether the Trump campaign coordinated with Moscow to help influence the race.