The former president decried New York County District Attorney Alvin Bragg for investigating the payment and criticised the US Department of Justice.
“The district attorney of New York under the auspices and direction of the Department of Injustice in Washington, DC, was investigating me for something that is not a crime, not a misdemeanor, not an affair,” he said.
“I never liked Horseface,” he said “I never liked ...”
Mr Trump continued by saying she would not be the person he would choose to cheat on his wife, former First Lady Melania Trump. Mr Trump is accused of having an affair shortly after Ms Trump gave birth to their son Barron.
“That would not be the one,” he said. “There is no one. We have a great First Lady.”
A grand jury in Manhattan has been hearing from witnesses about whether to indict the former president for the hush money payments. The former president had said last weekend that he would be indicted as early as Tuesday of this past week.
Mr Bragg called off the grand jury on 22 March and the grand jury did not hear from anyone on 23 March, delaying any potential indictment into next week.
In a letter to House Republicans, Mr Bragg said Mr Trump “created a false expectation that he would be arrested the next day and his lawyers reportedly urged you to intervene” and said a request from Republican lawmakers marked an “unprecedented inquiry into a pending local prosecution.”
Alex Woodward contributed to this report