"I would just say this with the president: There's an ongoing criminal investigation," Graham said on the CBS program "Face the Nation."

"You tweet and comment regarding ongoing criminal investigations at your own peril," he added.

On Sunday morning, Trump wrote on Twitter that he never asked former FBI Director James Comey to stop investigating Michael Flynn, the president's former national security adviser - a statement at odds with an account Comey himself has given.

That tweet followed one on Saturday in which Trump said: "I had to fire General Flynn because he lied to the Vice President (Mike Pence) and the FBI."

Legal experts and some Democratic lawmakers said if Trump knew Flynn lied to the Federal Bureau of Investigation and then pressured Comey not to investigate him, that could bolster a charge of obstruction of justice.

Trump's attorney, John Dowd, told Reuters in an interview on Sunday that he had drafted the Saturday tweet and made "a mistake" when he composed it.

"The mistake was I should have put the lying to the FBI in a separate line referencing his plea," Dowd said. "Instead, I put it together and it made all you guys go crazy. A tweet is a shorthand."

Dowd said the first time the president knew for a fact that Flynn lied to the FBI was when he was charged.