Drawing conclusions about President Trump's involvement in a scheme to make illegal payments to women based on federal prosecutors' claims in the case against Michael Cohen amounts to little more than "speculation," Republican Sen. John Thune of South Dakota told "Face the Nation" Sunday.

Federal prosecutors in New York on Friday said Cohen was acting at Mr. Trump's direction when Cohen illegally paid off two women who claimed they had affairs with Mr. Trump. The court filings do not directly accuse the president of a crime, and Mr. Trump insists he did not order Cohen to do anything illegal. Cohen has pleaded guilty to a variety of campaign finance and bank fraud charges, and admitted to lying to investigators about a proposed project to build a Trump Tower in Moscow.

Thune, who was recently elected to be the next majority whip by his Republican colleagues in the Senate, said it's important to wait until "additional evidence that comes out, and the special counsel, Robert Mueller, and his team continue to do their work."

"But I think at this point we have an incomplete picture, and I think at this point the president, as you know, as you said earlier, has denied some of these allegations that have been made," Thune continued. "Michael Cohen obviously has plenty of incentive now to cooperate and the representations that he makes, I think you have to, you know — there are going to be some questions raised about those as well. So I guess my view is that, let's wait. This thing is still not complete until it is complete. I think it's probably mostly speculation on the part of those of us who are not privy to all the details that the Mueller investigation are looking at."

As majority whip in the new Congress, Thune will soon be responsible for gathering and counting Republican votes in the Senate. He said the upper chamber has a very brief timeline to get things done before the new year. Mr. Trump is pushing for a vote on a criminal justice reform package, a priority of his son-in-law and senior adviser Jared Kushner. A handful of Republicans, including Sen. Tom Cotton, are reluctant to support the bill.

Thune offered no guarantees on being able to pass the legislation before the new year.

"There are several things that we have to do before the end of this year, before the next Congress starts," Thune said. "Criminal justice reform is an issue that we have a lot of members in our conference who support, but that's still being worked on and if it's going to be considered this year I think it's probably going to have to — they're going have to find a consensus that would enable it to move fairly quickly because we just don't have a lot of time."