In addition, one source confirms that Mueller's team wants information connected to the Oval Office meeting Trump had with Russian officials in which he bragged about firing Comey, saying it eased pressure on his White House.
Documents on Mr Trump's sacking of the Federal Bureau of Investigation director and his son's meeting with a Russian lawyer are the target of the inquiry, report U.S. media.
Mueller is asking the White House for documents related to some of Trump's most scrutinized actions while in office.
According to the Times, Mr Mueller has also asked for information regarding how the White House responded to questions from the newspaper about a meeting Mr Trump's eldest son, Donald Trump Jr, had with a Kremlin-connected attorney past year.
Trump's attorney responsible for providing requested documents to special counsel Mueller and congressional investigators, Ty Cobb told Mueller's office he will turn the documents over this week.
"What I can assure you is that we're fully cooperating with the special counsel, and we'll continue to do that", he said on "CBS This Morning".More news: Wenger denies confidence problems against big boys
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Photo Russia's official news agency photographed President Trump's meeting with Sergey V. Lavrov, the Russian foreign minister, in the Oval Office in May.
The list of categories from Mueller reads like a greatest hits of the Trump team's missteps. But it's his job to make sure all documents related to these requests are being found and sent to Mueller's team.
The retired lieutenant general was sacked in February after it was revealed he misled Vice President Mike Pence about December phone calls he had with the Russian ambassador at the time Sergey Kislyak. He officially resigned - reportedly at the request of the president - in February after his contacts with Russian Federation came to light.
Two bills that could curb the power of President Donald Trump's administration to fire special counsel Robert Mueller are set for a hearing in the Senate Judiciary Committee on Tuesday. Mueller has also asked for documents about how the White House responded to concerns raised by the Justice Department that Flynn might be subject to Russian blackmail for misleading Pence about the calls. "It obviously is relevant to his reasons for firing Comey, and thus to the obstruction investigation", O'Sullivan wrote.
In May, Rosenstein penned a memo criticizing then-FBI Director James Comey's handling of the investigation in Hillary Clinton's use of a private email server during her time as secretary of state.