Congressional probes related to alleged Russian meddling in the 2016 election are likely to be complicated or stalled by the appointment of former FBI director Robert S. Mueller III as a special counsel investigating the same topic, despite pledges by some lawmakers Thursday to forge ahead.

Mueller has resources and a mandate lawmakers know they cannot match and is the only one who can bring criminal charges — except against the president himself. Not responding to his subpoenas also comes with the real threat of criminal prosecution.

Sen. Lindsey O. Graham (R-S.C.), a member of the Senate Judiciary Committee, said his group would probably “have a hard time finding a lane now,” and that when it comes to his panel’s probe, Mueller’s appointment “probably well shuts it down.”

But other lawmakers leading committee probes contended that Mueller’s appointment would do nothing to affect the scope of their investigations.

“We’ve got a job to do, we’ve got an investigation to run and a report to write,” said Rep. K. Michael Conaway (R-Tex.), who is running the House Intelligence Committee’s probe. “I don’t believe it’ll have an impact on us at all.”

(Victoria Walker,Jayne Orenstein,Dalton Bennett,Jenny Starrs/The Washington Post)

But behind closed doors, lawmakers are growing increasingly nervous that with Mueller’s rise, their committee probes may be pushed aside — especially if he chooses to pursue a broad inquiry encompassing everything from the earliest allegations of Russian hacks to the circumstances that led to the firing of FBI Director James B. Comey.

Justice Department officials said Mueller would probably conduct his investigation almost entirely independent of Congress. But congressional investigators must take pains not to bump heads with the FBI’s inquiry. Committee leaders have already been having talks with senior Justice Department officials to “deconflict” their efforts — but lawmakers worry that if Mueller widens the scope of his investigation, they may have few witnesses at their disposal.

“Certainly, I think Congress’s ability to investigate this process fully is going to be hampered,” said Sen. Ron Johnson (R-Wis.).

“How can you subpoena somebody to come to Congress when they’re under criminal investigation? You can’t,” said Graham, lamenting that “one of the biggest losers of this decision is public access.”

The potential problems aren’t confined to witnesses. Lawmakers are also worried about being able to get access to information they need to continue their investigations.

During a briefing Thursday with Deputy Attorney General Rod J. Rosenstein, several senators on the Judiciary and Intelligence committees “raised concerns about access to information and processes that would be put in place for them to expeditiously get that information,” said Sen. Jeff Merkley (D-Ore.). “I didn’t hear anything that would give them assurance he would provide the access they need.”

Rosenstein will give House members a similar briefing Friday morning.

While Rosenstein didn’t ask senators to stand down — one member said he was “unequivocal” that the Senate Intelligence Committee should continue its probe — some members are bracing for at least a temporary slowdown while Mueller determines the breadth of his probe.

“It may mean that for a while, the congressional investigations will focus more on preparation for the 2018 and 2020 elections, consequences of Russian intrusion,” suggested Sen. Christopher A. Coons (D-Del.), a Judiciary Committee member. “That may be where we are for the short term, as Mueller makes his decision.”

As it stands, there are at least four congressional committees looking into roughly the same topic as Mueller: the House and Senate Intelligence Committees, the Senate Judiciary Committee and the House Oversight Committee. Each has sent letters requesting documents or called witnesses to testify.

But political considerations and leadership changes have complicated their efforts.

House Intelligence Committee Chairman Devin Nunes (R-Calif.) recused himself from that panel’s Russia probe after he was accused of coordinating the investigation with the White House. Then it took more than a month for the panel to announce its first public hearing after Conaway took over the investigation: an open hearing with former CIA director John Brennan on May 23 to discuss matters “related to Russian active measures during the 2016 election campaign.”

At the House Oversight and Government Reform Committee, chairman Jason Chaffetz (R-Utah) has also been quick to promise a reckoning, demanding records from the White House and declaring that “I have my subpoena pen ready” to compel Comey to turn over memos he kept about his discussions with Trump. But Chaffetz revealed Thursday that he is leaving Congress at the end of June. Rep. Trey Gowdy (R-S.C.), who is assisting Conaway’s leadership of the Intelligence Committee’s Russia probe, is the most likely to take his chairmanship.

Rep. Elijah E. Cummings (Md.), the ranking Democrat on the House Oversight Committee, is “on board” with those efforts to push ahead — but he acknowledged that congressional committees that rely on “part-time staff” cannot compete with the FBI probe.

“These are the kind of investigations where you need full-time people doing a full-time job,” he said.

But if Mueller’s appointment means Congress loses investigative ground, Republicans are blaming Democrats for clamoring for independent commissions and counsels in the first place.

“Democrats probably should be asking themselves, sometimes you’ve got to be careful what you ask for,” Johnson said. “It’s now an active investigation, there’s a special prosecutor in place, and I think we’ll have a more difficult time getting information for the intelligence committee.”

For now, the missions of Congress and Mueller are different: Mueller is examining the case with an eye on criminal charges, while Congress is looking into the matter to educate the public and consider legislation that might address the broader threat of Russian influence.

Mueller’s work, unlike Congress’s, should be completely secret, because he is using a grand jury and cannot legally release information from that proceeding unless there is a trial, said Jacob Frenkel, a former federal prosecutor now in private practice at Dickinson Wright. Frenkel worked previously in the Office of Independent Counsel — a type of special prosecutor no longer in use.

“The special counsel has no legal or other obligation to interface or interact at all with Congress about the substance of the investigation,” Frenkel said. “The fact is, he is running a grand jury, a federal grand jury investigation, all of the contents of which are protected.”

If Mueller’s investigation were to lead to Trump himself, the legislative branch’s role could become more significant if it came to consideration of impeachment proceedings. But that possibility is a long way off, lawmakers said.

“There are a lot of people that are talking about impeachment. I’m not talking about impeachment,” Cummings said. “I’m talking about let’s deal with that [Russian meddling] issue, because that’s a major threat to our democracy. Now where that leads, or things that may happen as we go, as these investigations go forward — I’m sure people like Mueller and others will take them into account.”

Ed O’Keefe contributed to this report.