WASHINGTON — Robert S. Mueller III, the special counsel, has asked the White House for documents about some of President Trump’s most scrutinized actions since taking office, including the firing of his national security adviser and F.B.I. director, according to White House officials.

Mr. Mueller is also interested in an Oval Office meeting Mr. Trump had with Russian officials in which he said the dismissal of the F.B.I. director had relieved “great pressure” on him.

The document requests provide the most details to date about the breadth of Mr. Mueller’s investigation, and show that several aspects of his inquiry are focused squarely on Mr. Trump’s behavior in the White House.

In recent weeks, Mr. Mueller’s office sent a document to the White House that detailed 13 areas in which investigators are seeking information. Since then, administration lawyers have been scouring White House emails and asking officials whether they have other documents or notes that may pertain to Mr. Mueller’s requests.