"It is important that Congress call the former FBI Director James Comey before the Judiciary Committee to obtain a full understanding of what President Trump may or may not have done regarding the Russian investigation, including General Michael Flynn," Graham said.
The sooner Comey testifies before the committee, the better it will be for the country, the senator noted.
On Tuesday, The New York Times newspaper reported that Trump, during a meeting with Comey at the White House in February, told the then FBI director to stop the Bureau's investigation into former National Security Adviser Michael Flynn and his ties with Russia.
The White House has denied the allegations, stressing that Trump has never asked Comey or any other official to halt the investigation.
The Democrats from both congressional committees asked the FBI in their letter to hand over Comey's memo by May 24.
On May 10, Trump fired Comey and said in several subsequent interviews that he had decided to remove him months ago.