The Justice Department's decision to establish a special counsel to investigate possible links between Russia and the Trump administration placated many lawmakers, but it's also leading to new fears among senators that the move will render moot any effort by Congress to investigate these issues.

Deputy Attorney General Rod Rosenstein named former FBI Director Robert Mueller as special counsel on Wednesday and met with senators from both parties on Thursday to explain the move. But senators on the way out of that meeting indicated they have several new worries about the Senate investigation being overtaken by Mueller's.

One worry is whether Mueller will communicate any information at all to Congress about how he's proceeding. Sen. Chris Coons, D-Del., said that could leave the Senate Intelligence Committee in the dark about whether and how it can carry out its own investigation.

"My concern is that we not end up in a place where special counsel doesn't communicate to Congress for months, or years, a decision he's made about the scope of the investigation," Coons said shortly after leaving the briefing.

"I think those decisions about the scope of the investigation need to be made relatively quickly so that congressional investigations can either proceed or pursue other matters," Coons added.

Another possible problem outlined by senators is whether Mueller will be seeking criminal charges as part of its probe. Several senators said it would be up to Mueller to make that call, but Sen. Lindsey Graham, R-S.C., said his impression was that Mueller would be seeking criminal charges, which could make it hard for any congressional committee to hear testimony on its own.

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

"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 added. "If I were Mr. Mueller, I would jealously guard the witness pool."

A senior Senate aide echoed the sentiments and said there's a good chance that lawmakers will be removed from the equation altogether, forcing them from the playing field and into the spectator stands as they watch Mueller work, possibly for years. That aide, who requested anonymity, was working in Congress during Ken Starr's investigation of the Clinton administration.

Sen. Marco Rubio, R-Fla., said he's hopeful that there can still be some work for Congress while Mueller's investigation proceeds. He and other senators indicated after the Rosenstein meeting that Congress has approached the matter as a counter-intelligence issue, in order to assess the extent to which a foreign power interfered with the U.S. election.

Rubio said he was hopeful that work could continue without conflicting with Mueller, who may end up focusing on whether any laws were broken, and possible criminal charges.

"The counterintelligence matter moves forward, and it is my hope that they will not be in conflict with one another, and I do not believe that they need to be in conflict with one another," Rubio said.

Russia-related investigations have been taking place for months now in the House and Senate intelligence committees, which have taken testimony in a series of open and closed door hearings. Additionally, the Senate Judiciary Committee has oversight related to the FBI and the DOJ, which has given it a chance to explore the issues surrounding Russia and the Trump administration.