President Trump's attorney Rudy Giuliani says President Trump did nothing wrong in his dealings with Michael Cohen and isn't worried about testimony he might give to special counsel Robert Mueller.

The only legal risk for Mr. Trump, Giuliani told CBS News' Paula Reid, is lying to investigators, which Giuliani says could only be proven by a witness or document giving an alternate version of events. That's one reason Giuliani is pushing for the Mueller investigation to reach its conclusion.

Cohen, who was known as Mr. Trump's fixer, is currently under criminal investigation by the Justice Department.

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Whether Mr. Trump will testify is still an open question, Giuliani told Reid. He said Mueller is not currently insisting on an interview with Mr. Trump. But any testimony would come before Cohen's decision to cooperate, and would be too late to implicate the president, he said. Despite that thinking, the Justice Department could still issue charges related to the investigation if new evidence emerges.

Giuliani made a similar argument with respect to former Trump campaign chairman, Paul Manafort, who is in a Virginia jail awaiting trial on numerous alleged financial crimes.

On ABC's "This Week" on Sunday, Giuliani stressed that he wasn't worried about testimony that Cohen might give.

"Michael Cohen should cooperate," Giuliani told host George Stephanopoulos. "The president did nothing wrong with him. As long as he tells the truth, we're home free."

Mr. Trump has been particularly outspoken about the special counsel investigation on Twitter lately, calling the probe a "Rigged Witch Hunt" on Saturday. Giuliani said Mr. Trump's tweets are the result of the president finally having the time to turn his attention to this issue and because Mr. Trump wants the investigation to wrap up.

Giuliani told The New York Times on Friday that Mr. Trump's legal team is demanding Mueller prove he has evidence Mr. Trump committed a crime before the president agrees to an interview. He clarified on ABC that he wants to confirm that there is a "factual basis for the investigation."

Giuliani also discussed whether Mr. Trump's Supreme Court nominee should be involved with the Mueller investigation and Mr. Trump's upcoming meeting with Russian President Vladimir Putin.

Mr. Trump is expected to announce his Supreme Court justice nominee on Monday. Giuliani said he does not think Mr. Trump's pick should be recused from any case involving a presidential subpoena from Mueller, an issue Democrats have raised.

Later this month, Mr. Trump will be meeting with Putin in Helsinki. Giuliani said he is not worried about the optics of such a meeting, despite the special counsel investigation into Russian meddling in the U.S. election.