Mr Trump, in his tweet, declared: "As has been stated by numerous legal scholars, I have the absolute right to PARDON myself, but why would I do that when I have done nothing wrong?"
Can a president pardon himself? An attorney for Mr Trump is playing down the possibility that he would try to - if it came to that.
Rudy Giuliani has escalated attacks on the Department of Justice.
Photo: APMr Giuliani said Mr Trump might have that authority but exercising it would be "unthinkable." Besides, Mr Giuliani, added, Mr Trump has done nothing wrong and has no need to consider pardoning himself.
The question of whether a president can self-pardon has long been a "parlor game" among scholars, said Jonathan Turley, a constitutional law professor at George Washington University Law School.
There's no precedent for it and thus no case law. Mr Turley said he believes a president can pardon himself - but added that would not protect a president from impeachment.
"A president cannot pardon out of an impeachment," Mr Turley said. Congress, he said, "can use his pardon as an abuse of his office."
Mr Giuliani's comments come as the White House sharpens its legal and political defenses against the special counsel Russia probe.
He made it clear that Mr Trump's legal team would combat any effort to force the president to testify in front of a grand jury.