He said in a tweet: "I did not make, and do not have, any such recordings."
Days after he fired Mr Comey in May, the president had tweeted: "James Comey better hope that there are no 'tapes' of our conversations..."
He has been under pressure to produce the tapes amid inquiries into alleged Russian meddling in the election.
The House Intelligence Committee had earlier this month asked the White House to hand over any such recordings.
James Comey was heading the FBI inquiry into alleged Russian interference in last year's presidential election, and whether the Trump team had any links to Moscow, when he was fired on 9 May.
In the days that followed, a succession of stories appeared in US newspapers with allegations surrounding a private meeting Mr Trump had with Mr Comey in the Oval Office in February.
They included the claim that the president had asked Mr Comey to drop an investigation into fired National Security Adviser Mike Flynn.
It was in that context that Mr Trump sent his tweet, hinting that there were tapes of the conversation.
Appearing before Congress earlier this month, Mr Comey confirmed he had been asked by the president to "let go" any possible prosecution of Mr Flynn for lying to federal agents about a conversation with the Russian ambassador.
He said he was also asked by the president in no uncertain terms to give assurances that he would be loyal.
When asked whether he thought the conversation had been recorded, Mr Comey replied: "Lordy, I hope there are tapes."

Seven members have not yet turned up, allegedly because of transport issues.
But there are suspicions the Algeria team wanted to boycott the match against Israel because of longstanding tensions between the two countries.
Goalball is a sport for the visually impaired involving a ball with bells.
Algeria had been due to play the US on Friday, and Israel on Saturday, and the seven team members were scheduled to leave a training camp in Poland for Rio last Monday.
The IPC says the team claims to have missed a bus which led to them missing a flight. They allegedly did not manage to rebook it in time because of a public holiday in Algeria.
"It's an interesting account they have delivered to us," IPC spokesman Craig Spence told the BBC.
"To have five days travelling to Rio, it's a long time. I've missed connections in the past, and you usually get there within 24 hours," he said.
Goalball at the Rio 2016 Paralympics: All you need to know
A beginner's guide to goalball
The Times of Israel suggests the Algerian absence is "likely to avoid an Israel draw".
"It is a great shame that politics has also seeped into the Paralympics," the paper quotes the head of the Israeli Paralympic Committee, Danny Ben-Abu, as saying.
The issue has received some reaction on social media too.
The IPC says it will check the facts and act accordingly.
"If, as many people believe, this is a political protest, we can take some form of action against them," Craig Spence says.
"It could be a slap on the wrist, or we could remove the goalball team from the tournament altogether," he added.
In the meantime, both the US and Israel have been awarded a 10-0 win and three points each for the unplayed matches.
Goalball is played by two teams of three visually impaired players, using a ball with bells inside.  The object of the game is to throw the ball into the opposing team's net, while defenders attempt to block it with their bodies.
US President Donald Trump says he did not make secret recordings of ex-FBI chief James Comey despite an earlier hint to the contrary.
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The International Paralympic Committee (IPC) has said it is investigating why the Algerian women's goalball team failed to arrive in Rio in time for matches against the US and Israel.