Trump was addressing reporters at the White House for the first time since Comey's explosive appearance, in which he branded the president a liar and said he believed he was sacked over his handling of the Federal Bureau of Investigation probe into Russian election meddling.
Mr Trump's aides have dodged questions about whether conversations relevant to the Russian Federation investigation have been recorded, and so did the president in a series of teases.
Comey repeatedly refused to say in the Senate hearing Thursday whether he thought Trump had obstructed justice.
A member of Trump's legal team, Jay Sekulow, told ABC today that Trump would "address the issue of the tapes, whether the tapes exist or not, next week".
James Comey giving testimony. Then he said he is never going to release them.
Trump and his defenders have seized on a portion of Comey's Thursday testimony before the Senate Intelligence Committee in which he said he allowed a friend to share a memo with the press about his conversation with Trump, hoping it would trigger the appointment of a special prosecutor.
Mr Lankford said Mr Sessions's testimony will help flesh out the truth of Mr Comey's allegations, including Mr Sessions's presence at the White House in February when Mr Trump asked to speak to Mr Comey alone.
"I'll tell you about that sometime, maybe in the very near future", Trump said. During his campaign, Trump often said it was time to "drain the swamp" in Washington of corrupt and self-dealing insiders. They also made a formal request to the Comey camp for copies of the memos he testified he made to document the meetings.
On Friday, Trump indicated that he was willing to do that, a highly unusual step for a sitting president and one fraught with legal hazard.
The leaders of the House of Representatives intelligence committee said they have written to Comey, and also Don McGahn, the White House counsel, and asked him whether White House recordings or memos of Comey's conversations with Trump exist.
Republican Senator Susan Collins called today for Trump to "voluntarily turn them over" to the Senate Intelligence Committee and to the special counsel, Robert Mueller, investigating possible collusion between Trump aides and Russian Federation. You fired him to stop him.
Comey told the Senate intelligence committee he hoped the move would trigger the appointment of a special counsel to investigate Russian interference in the US presidential election.
"We all want to know all of the information, but keep in mind, that his job is to determine whether or not there are any violations of criminal laws, and he wants to make sure that he has all the evidence put together, rather than releasing it in a piecemeal basis", the senator said. "Why do you think he's colluding with the Russians?"