Trump is responding to the revelation that attorney Michael Cohen made a secret recording of their discussion about a potential payment for a former Playboy model's account of having an affair with Trump.
He also called raids of Cohen's home, office and hotel room earlier this year "inconceivable" and "almost unheard of".
"Inconceivable that the government would break into a lawyer's office (early in the morning) - nearly unheard of", Trump wrote on Twitter Saturday morning.
The recording about the former Playboy model, Karen McDougal, which occurred prior to the election, was among the troves of documents and materials that the FBI seized from Cohen's office, home and hotel in NY back in April amid a criminal investigation of Cohen by the U.S. attorney's office for the Southern District of NY.
Earlier this year, in an interview with CNN, McDougal detailed what she said was a 10-month affair she had with Trump in 2006 and 2007.
Cohen recorded the conversation with Trump, which was seized by federal agents now investigating Trump's longtime confidant for potential bank and campaign finance crimes, according to multiple familiar with the probe.
Davis said "any attempt at spin can not change what is on the tape".
In a statement Friday (Saturday NZT), President Trump's attorney Rudolph Giuliani confirmed the tape's existence and said no payment was ever made.
He later told the New York Times that the two men had in fact spoken about paying the Enquirer for rights to the story, thereby repaying the tabloid the amount it had given to Ms McDougal.
Mr Trump had previously denied all knowledge of the $130,000 payment to porn actress Stormy Daniels as part of a non-disclosure agreement. Citing a source familiar with the tapes, CNN reported that Trump, when informed about the September 2016 tape, said, "I can't believe Michael would do this to me". David Pecker, the chairman of parent company American Media Inc (AMI), is Trump's friend.
Giuliani had earlier denied Trump had an affair with McDougal.
Non-disclosure agreements of the type signed by Ms Daniels and allegedly by Ms McDougal are not in themselves illegal. However, 11 states, including Florida, where Trump spends a lot of time, do require both people in a conversation are aware a recording is taking place.
To pursue criminal charges against Cohen for breaking federal election law, prosecutors would have to have evidence that the payments went to the women to influence the election, rather than just to protect Trump personally.