Sen. Marco Rubio is reserving judgment on President Trump's alleged connection to the criminal case against former longtime attorney Michael Cohen. Asked on "Face the Nation" whether he stands by the president, the Florida Republican said he sees "no reason not to stand by anybody in this moment."

Prosecutors in federal court in New York claimed in a court filing Friday that Cohen acted "at the direction of" Mr. Trump during the 2016 campaign when he arranged illegal payments to women who said they had sexual encounters with the real estate mogul. Mr. Trump, asked by reporters Saturday whether he directed Cohen to do anything illegal, responded, "No, no, no."

Rubio did not directly respond when first asked whether he stands by the president after prosecutors suggested Mr. Trump was connected to the crimes to which Cohen has pleaded guilty.

"Look, we're a nation of laws," Rubio responded. "We have a system by which a government can acquire information, put that information and evidence together and make presentations before judges."

Pressed a second time whether he continues to stand by the president, Rubio emphasized again the importance of letting the process play out.

"Well, again, there's nothing — there's no reason to not stand by anybody in this moment," Rubio said. "There are pleadings, there are cases, there are evidence. We're going to wait for all of it to be out there. And I would caution everyone to wait for all of it to be out there until you make judgment. Your judgment may not change, but nonetheless judgments should be made on the basis of all the information that is before you. That is most certainly what we're doing in the U.S. Senate Intelligence Committee. So, as I've said repeatedly I believe that Mr. Mueller's probe should continue and move forward unimpeded."

Cohen is scheduled to be sentenced in federal court Wednesday. He pleaded guilty this summer to eight federal charges over the summer, including campaign finance violations and tax fraud. He has also pleaded guilty to revelations from Mueller's office that he misled Congress about considerations to build a Trump Tower in Moscow.

Mr. Trump said he wants Cohen to serve a "full and complete" sentence for crimes alleged by Mueller's office.