Comey wrote memos about his recollection of those events because he said Thursday he did not trust the president to tell the truth about their conversations.
Trump Jr also said Comey's testimony "vindicated" the president and that everything in it was "basically ridiculous".
The message was the Trump's first since Wednesday - a day before Comey's testimony before the Senate intelligence committee that riveted the nation.
Several reporters shouted follow-up questions on the existence of the tapes after Trump's non-answer. They also disputed Comey's assertion that Trump asked the Federal Bureau of Investigation director for a pledge of personal loyalty to the president.
"I woke up in the middle of the night on Monday night, because it didn't dawn on me originally, that there might be corroboration for our conversation, there might be a tape", Comey said.
"I would be glad to tell him exactly what I just told you, Jon", Trump responded.
"You and I are friends: "Hey, I hope this happens, but you've got to do your job".
The Six-Day War that changed Palestinian history
The Israeli and Palestinian leadership have come close to peace on few occasions, with both parties refusing to compromise on several key issues, causing a stalemate.
President Donald Trump listens during a news conference with Romania's President Klaus Werner Iohannis in the Rose Garden of the White House in Washington, Friday, June 9, 2017.
"I believe the James Comey leaks will be far more prevalent than anyone ever thought possible. Absolutely, I'd be committed to Article 5".
Trump tweet: Despite so many false statements and lies, total and complete vindication...and WOW, Comey is a leaker!
During his testimony Thursday, Comey told lawmakers that Trump was not a target in the bureau's investigation into Russian Federation. Trump stopped short of saying that Comey lied under oath.
Comey, who was sacked by Trump in May, delivered a scathing indictment of the president on Thursday at a congressional hearing in which he accused Trump of trying to block the investigation into Flynn. American intelligence agencies have said it was an effort by the Kremlin to help Trump defeat his Democratic opponent, former Secretary of State Hillary Clinton.
Sacked FBI chief Comey delivered his bombshell allegations at a Senate hearing Thursday, saying in his sworn testimony that he had asked a "friend" identified as a Columbia University law professor to release a memo of his conversations with the president to the press.
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