On Wednesday, Mueller is scheduled to appear at back-to-back hearings before the Democratic-led House of Representatives Judiciary Committee and Intelligence Committee to discuss his inquiry into Russia's role in the 2016 US election, contacts between the Trump campaign and Moscow, and the Republican president's efforts to impede the investigation.

Associate Deputy Attorney General Bradley Weinsheimer wrote in a letter to Mueller on Monday that the former FBI director's testimony must remain within the boundaries of the 448-page special counsel investigative report the department released in redacted form on April 18.

Weinsheimer wrote that some matters covered by the inquiry were covered by "executive privilege", a legal principle rarely invoked by US presidents to keep other branches of government from getting access to certain internal executive branch information.

It generally is used to keep private internal discussions between the president and his advisers.

House Judiciary Committee chairman Jerrold Nadler said Mueller did not need to follow the instructions contained in the letter.

"He does not have to comply with that letter. He doesn't work for them. And that letter asks things that are beyond the power of the agency to ask even if he still worked for them," Nadler said in a CNN interview.

Nadler said he does not think the letter posed any impediment to members of his committee.

"I think it's incredibly arrogant of the department to try to instruct him in what to say," Nadler added. "It's part of the ongoing cover-up by the administration to keep information away from the American people."

A spokesman for Mueller, Jim Popkin, said the letter had been received but declined further comment.

The Trump administration has instructed other former officials not to co-operate with some other congressional investigations.

Democratic lawmakers are expected to try to get Mueller to focus on specific examples of Trump's conduct that they consider improper.

Democrats are deeply divided over whether to pursue the impeachment process set out in the US Constitution for removing a president from office.

Mueller's report outlined Russia's actions to interfere in the election with a campaign of hacking and propaganda aimed at boosting Trump's candidacy and detailed the Trump campaign's willingness to benefit from Moscow's actions.

The report said the inquiry found insufficient evidence to conclude that Trump and his 2016 campaign engaged in a criminal conspiracy with Russia despite the numerous contacts. The report did not reach a conclusion on whether Trump committed the crime of obstruction of justice but did not exonerate him.

Attorney General William Barr, a Trump appointee, subsequently said the president had not committed obstruction of justice. Longstanding Justice Department policy bars criminal charges against a sitting president.

Australian Associated Press