Sen. Lindsey Graham, R-S.C., said Thursday that the appointment of a special counsel to investigate Russia's meddling in the election will significantly hamper efforts by congressional committees to run their own parallel investigations.

Graham also said after the all-Senate briefing with Deputy Attorney General Rod Rosenstein that his impression is that special counsel Robert Mueller is running a criminal investigation, not a counterintelligence investigation. However, other senators who left the meeting said it would be up to the newly named special counsel, former FBI Director Robert Mueller, to decide that.

Regardless, Graham said that possibility could make it harder for congressional committees to gather their own evidence.

"I think the shock to the body is, it's now considered a criminal investigation, and Congress's ability to conduct investigation of all things Russia has been severely limited, probably in an appropriate fashion," Graham told reporters.

"So I think a lot of members want the special counsel to be appointed, but don't understand that ... you're pretty well knocked out of the game. And that's probably the way it should be," he said.

Graham explained that House and Senate committees will likely find their own witnesses less informative if there is any chance they will have to testify in a criminal probe.

"I find it hard to subpoena records of somebody like Mr. [Mike] Flynn, who may be subject to a criminal investigation because he has the right not to incriminate himself," he said. "If I were Mr. Mueller, I would jealously guard the witness pool."

"So one of the big losers in this decision is the public," he said.

Trump on Thursday morning said the ongoing investigations into Russia are a "witch hunt." But when Sen. Marco Rubio, R-Fla., was asked about that comment, Rubio answered, "we are a nation of laws."