Rudy Giuliani, the former mayor of New York City, is now part of Donald Trump's legal team | Zakaria Abdelkafi/AFP via Getty Images Giuliani: ‘Truth isn’t truth’ Trump lawyer tries to clarify why the president should not testify for special counsel Robert Mueller.

President Donald Trump's lawyer Rudy Giuliani on Sunday claimed "truth isn't truth" when trying to explain why the president should not testify for special counsel Robert Mueller for fear of being trapped into a lie that could lead to a perjury charge.

“When you tell me that, you know, he should testify because he’s going to tell the truth and he shouldn’t worry, well that’s so silly because it’s somebody’s version of the truth. Not the truth,” Giuliani told Chuck Todd on NBC’s “Meet the Press” on Sunday morning

“Truth is truth,” Todd responded.

“No, it isn’t truth,” Giuliani said. “Truth isn’t truth. The President of the United States says, “I didn’t …”

A startled Todd answered: “Truth isn’t truth?”

Giuliani: “No, no.”

Todd said: “This is going to become a bad meme.“

Giuliani‘s remark is not the first time he has gone down this road. Last week on CNN, he rejected Chris Cuomo’s assertion that “facts are not in the eye of the beholder."

"Yes, they are," Giulini said. "Nowadays they are."

Trump's legal team, led by Giuliani, earlier this month replied to special counsel Mueller’s proposal for terms of a possible presidential interview, but wouldn't disclose the details of the counteroffer.

Mueller is investigating whether the Russian government colluded with Trump's 2016 campaign, as well as related issues including possible obstruction of justice by the president.

The president has said he is willing to speak with the special counsel, though his legal team is advising against it.

Giuliani also accused Mueller of leaking that White House counsel Don McGahn cooperated with the special counsel.

The New York Times reported Saturday that McGahn spent 30 hours over a three-day period answering questions as part of Mueller's investigation.

Trump tweeted Saturday evening that he allowed McGahn and "all other requested members of the White House staff, to fully cooperate with the special counsel.”

Giuliani told Todd that the special counsel is the only one who could have "leaked" the story.

"I believe this is a desperate special council who leaked this to the New York Times, illegally I might add," he said.

When pressed how he knew it was Mueller, Giuliani said those involved on Trump's side would have never done it.

"I didn't leak to the Times and Jay Sekulow didn't leak it to the Times. The president sure as heck didn't. So who could it be?" Giuliani said. "It could be McGahn. McGahn's not doing it and he would have done it a long time ago if he was gonna do it."

Giuliani, who has previously called on the investigation to end in September, said he doesn't believe the White House has any evidence on the president.

"They're down to desperation time," he said. "They have to write a report and they don't have a single bit of evidence."