But, Giuliani argued, it's fine for him to do that because he was not under oath.
Giuliani, speaking to ABC's George Stephanopoulos , admitted that Trump's account of payments made to women who say they had sexual relationships with the president, had changed four or five times over the course of an investigation.
But, according to Giuliani, the evolving story owed to lapses in Trump's memory, which he characterized as common and expected.
Giuliani on ABC consistently attacked Michael Cohen, Trump's former lawyer who was recently sentenced to 3 years in prison after admitting to an array of crimes he committed while working for Trump, as a liar.
Cohen told the court that Trump directed him to pay off women who alleged sexual relationships with the president in what the judges saw as a campaign finance violation.
Cohen had previously denied making the payments, and then denied that Trump had anything to do with them. Trump also initially denied the payments, and has since offered differing accounts of how they were paid out.
As he was sentenced last week, Cohen said he had broken the law out of "blind loyalty" to Trump. Giuliani called that a lie, saying Cohen had taped conversations with Trump, which showed that the loyalty was not total.
Giuliani, suggesting that the US Attorney for the Southern District of New York had offered Cohen a reduced sentence in exchange for implicating Trump, said that Cohen was highly motivated to blame Trump for the crimes.
"There's a real motivation to sing like crazy, you've got to do a lot of singing to get out of the three years," said Giuliani. "He will say whatever he has to say, he's changed his story four or five times," he continued.
"So has the president," interjected Stephanopoulos.
"The president's not under oath," said Giuliani, without making an effort to deny that Trump had changed his story on the payments and often contradicted himself in factual terms.
"The president is doing the best he can to try and remember what happened," he continued, suggesting that Trump had told mistruths about the sequence of events involving Cohen's crimes.
But Giuliani chalked up Trump's shifting stories to a simple matter of flawed memory.
"He was the busiest man in the world. I was with him most of that time. I can't remember a lot of the stuff that goes on there," Giuliani continued.
Watch the full interview here .