President Donald Trump's lawyer Rudy Giuliani said on NBC's "Meet the Press" Sunday he doesn't want Trump to be caught in a perjury trap by speaking with the special counsel Robert Mueller.

Giuliani said an interview with Mueller as part of the probe into Russian interference in the 2016 election could be a trap, because "truth isn't truth."

The special counsel's push to talk to Trump is a publicity ploy, Giuliani said, as they are "desperate for some kind of charge they can hang their hat on."

It was recently reported Trump's legal team is prepared to oppose a subpoena from Mueller.

President Donald Trump's lawyer Rudy Giuliani said on NBC's "Meet the Press" Sunday he didn't want his client to testify in the special counsel Robert Mueller's investigation to avoid committing perjury.

Giuliani told host Chuck Todd that an interview with Mueller as part of the probe into Russian interference in the 2016 election could be a trap, because "truth isn't truth."

"I'm not going to be rushed into having him testify so that he gets trapped into perjury," Giuliani said. "When you tell me that 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."

"Truth is truth," Todd interjected.

"No, it isn't truth. Truth isn't truth," Giuliani said.

"Truth isn't truth?" Todd asked, putting his head in his hand. "Mr. Mayor, do you realize what ...? This is going to become a bad meme."

"No, no, no, don't do this to me," Giuliani said, mimicking Todd's exasperated touch to his forehead.

"Don't do 'truth isn't truth' to me," Todd replied.

"Donald Trump says 'I didn't talk about Flynn with Comey.' Comey says 'you did talk about him.' So tell me what the truth is," Giuliani said, later adding, "We have a credibility gap between the two of them. You've got to select one or the other. Now who do you think Mueller is going to select?"

—Meet the Press (@MeetThePress) August 19, 2018

Giuliani also railed against the investigation as a whole, including Mueller's look into whether Trump sought to obstruct justice in the investigation and discussing White House counsel Don McGahn, who was revealed Saturday to be a critical witness in the obstruction inquiry.

The New York Times reported McGahn has sat for over 30 hours of special counsel interviews in recent months, which Trump tweeted Sunday morning he "allowed" McGahn to do. But a person familiar with the matter told The Times McGahn thought Trump was going to make him the fall guy in the probe, so he gave Mueller's team critical details about Trump's actions to try and control the investigation.

Giuliani said Trump's team "have a good sense" of what McGahn told the special counsel, and that Trump has nothing to hide, as he maintains his "true belief that he did nothing wrong, that he wasn't involved in collusion, that he wasn't involved in obstruction."

Referencing remarks by another one of Trump's lawyers, John Dowd, Giuliani said he believed "McGahn was a strong witness for the president," downplaying possible concerns that McGahn could be a strong witness against Trump. But Giuliani said he hasn't debriefed McGahn himself about his hours of interviews with Mueller's team.

The special counsel's push to talk to Trump is a publicity ploy, Giuliani said, as "the only reason they could possibly want the president of the United States is because they are desperate for some kind of charge they can hang their hat on. They don't have collusion or conspiracy."

"How do you know that?" Todd asked.

"This whole McGahn thing leaked from them," Giuliani said. "If they had some kind of evidence that there was collusion or there was obstruction, don't you think it would have been leaked? They leak everything else."

McGahn is a valuable witness in the obstruction inquiry, given his knowledge of several key moments throughout the Russia investigation since his appointment in May 2017.

The Washington Post reported last week that Trump's lawyers are prepared to oppose a subpoena from Mueller, which would mean the president must sit with the special counsel for an interview.

In a brief text message exchange last week with Business Insider's Allan Smith, Giuliani explained how the president's legal team would argue that such a subpoena would be unconstitutional, citing past arguments that a sitting president cannot be indicted.

Watch Giuliani's full interview below: