News of the cooperation deals came days after former Trump lawyer Michael Cohen pleaded guilty to eight crimes, including two counts related to hush money paid just before the 2016 election to women who alleged affairs with Trump. Cohen said he made the payments at Trump's direction.
The Cohen case is unlikely to lead to any legal consequences for Trump while he is in office, experts say, although it could prompt calls for his impeachment should Democrats retake the House in November.
Dershowitz said that "it would be great" to have Democrats in charge on Capitol Hill so that they can conduct investigations into Trump's actions.
But he continued to play down Trump's failure to report the hush money, arguing that the person at fault for the campaign finance violation would be the campaign's treasurer, not the candidate.
"The president or the candidate is entitled to contribute anything he wants to his own campaign," Dershowitz said. "So the only issue here is whether or not there was a failure to report the contribution. That failure to report is attributable to the treasurer of the campaign, not to the president."
Weighing in on whether Trump should sit for an interview with Mueller, Dershowitz contended that "it would be good for the American public if President Trump sat down and said everything he knows, but it wouldn't be good for President Trump. And that's why his lawyers are so strongly recommending against it."
He also offered four broader points of advice for Trump.
"Look, my advice to the President, I never gave it to him privately because I'm not his lawyer, but on television is: Don't fire, don't pardon, don't tweet and don't testify. And if he listened to those four things, he'd be in less trouble than he is today," Dershowitz said.
In an interview on Fox News Sunday, former attorney-general Alberto Gonzales said that Cohen's guilty plea and the conviction of former Trump campaign chairman Paul Manafort were creating "a lot of debate and swirl around the President as an individual, and that's never good."
Trump has praised Manafort and recently sought his lawyers' advice on a potential pardon, according to Trump lawyer Rudy Giuliani. Gonzales said that while Trump is entitled to speak his mind, his apparent sympathy for Manafort puts him at odds with his own Justice Department.
"They had a very successful conviction of Paul Manafort. And to have the President then, you know, speak so well of Paul Manafort was somewhat unusual," Gonzales said.
He added that it might be helpful for Trump to at least answer written questions from Mueller in the Russia probe, even if he declines to provide oral testimony.
"I think perhaps it may ease, in the minds of certain members of the American public, the President's involvement, the President's knowledge about Russian involvement" in the 2016 presidential election, Gonzales said.
