The argument was laid bare this week during former White House chief strategist Steve Bannon's interview with the House Intelligence Committee.
Lawmakers on the committee were fuming after Bannon reportedly wouldn't answer any questions about his time in the White House or during the transition to the White House after Trump's presidential win.
In the book, Bannon is quoted as describing a June 2016 meeting between Trump associates, including the president's son Donald Trump Jr., his son-in-law, Jared Kushner, and a Russian lawyer, as "treasonous" and "unpatriotic".
Bannon was sacked from his White House job in August as the president sought to bring more order to his staff operations. His first appearance was voluntary and Bannon's representatives have made no comment.
Mueller is investigating any potential collusion by Trump's campaign with Moscow in alleged Russian meddling in the 2016 election. "I would be happy to come in and sit down". Six days later, Bannon stepped down as executive chairman at Breitbart News.
Separately on Tuesday, Bannon spent hours meeting behind closed doors with the House of Representatives Intelligence Committee.
A House committee aide declined comment on media reports that Bannon could return to testify again as soon as Thursday.
Steve Bannon was sacked from his White House job in August as the president sought to bring more order to his staff operations.
President Donald Trump's White House is relying on a sweeping interpretation of executive privilege as current and former advisers parade to Capitol Hill for questioning about possible connections with Russian Federation.
On Wednesday, White House press secretary Sarah Sanders said the White House was cooperating with the congressional investigations.
It comes after two previous committee interviews didn't go so well.
Later in the week, the panel will hear from former Trump campaign manager Corey Lewandowski.
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