WASHINGTON — White House officials asked at least twice in the past month for the key witness against President Trump in the Mueller report, Donald F. McGahn II, to say publicly that he never believed the president obstructed justice, according to two people briefed on the requests.

Mr. Trump asked White House officials to make the request to Mr. McGahn, who was the president’s first White House counsel, one of the people said. Mr. McGahn declined. His reluctance angered the president, who believed that Mr. McGahn showed disloyalty by telling investigators for the special counsel, Robert S. Mueller III, about Mr. Trump’s attempts to maintain control over the Russia investigation.

[Update: Federal judge rules that Donald McGahn must testify before Congress.]

The White House made one of the requests to Mr. McGahn’s lawyer, William A. Burck, before the Mueller report was released publicly but after the Justice Department gave a copy to Mr. Trump’s lawyers in the preceding days. Reading the report, the president’s lawyers saw that Mr. Mueller left out that Mr. McGahn had told investigators that he believed the president never obstructed justice. Mr. Burck had told them months earlier about his client’s belief on the matter and that he had shared it with investigators.

Mr. McGahn initially entertained the White House request. “We did not perceive it as any kind of threat or something sinister,” Mr. Burck said in a statement. “It was a request, professionally and cordially made.” A White House spokeswoman did not respond to a message seeking comment.