(Peter Stevenson,Jason Aldag,Whitney Leaming/The Washington Post)

Congressional investigations into Russian interference in the 2016 election will continue despite the Justice Department’s decision to appoint a special counsel to oversee a separate probe, lawmakers said late Wednesday.

Republicans and Democrats welcomed the decision to appoint Robert Mueller, a former prosecutor who served as FBI director from 2001 to 2013, but said their own investigations would proceed without delay.

“Our task hasn’t changed,” Senate Intelligence Committee Chairman Richard Burr (R-N.C.) told reporters.

“This is a good decision,” he said of Mueller’s appointment. “By having someone like Bob Mueller head whatever investigation assures the American people that there’s no undue influence — be it here or be it at the other end of Pennsylvania Avenue or within the Justice Department or FBI.”

Deputy Attorney General Rod J. Rosenstein will brief the full Senate Thursday on Trump’s firing of FBI Director James B. Comey — an event that triggered a wave of controversy for the White House starting last week.

(Jenny Starrs/The Washington Post)

Congressional Republicans had spent much of Wednesday increasing pressure on the administration to produce records related to the latest string of controversies involving Trump, amid flagging confidence in the White House and a growing sense that scandal is overtaking Trump’s presidency.

Speaker Paul D. Ryan (R-Wis.) said his priority is to ensure investigations “follow the facts wherever they may lead.”

“The addition of Robert Mueller as special counsel is consistent with this goal, and I welcome his role at the Department of Justice,” he said in a statement.

Attention on Capitol Hill is now expected to focus on when Comey might testify publicly before lawmakers.

Comey, who was leading an investigation into Russia before Trump fired him last week, wrote in a memo that Trump had pressured him to drop an investigation against former White House national security adviser Michael Flynn earlier this year.

In a nod to strong interest from lawmakers, Burr and ranking Democrat Mark Warner (Va.) asked Comey on Wednesday to testify in both open and closed sessions.

(Bastien Inzaurralde,Jayne Orenstein,Dalton Bennett,Alice Li,Whitney Leaming/The Washington Post)

House Oversight and Government Reform Committee Chairman Jason Chaffetz (R-Utah) also invited Comey to speak at a hearing next Wednesday.

Praising Mueller’s “impeccable credentials,” Chaffetz said his panel’s efforts to probe Trump will continue.

“We’re still moving full steam ahead,” Chaffetz he told The Washington Post. “We will still want to see the memos and I’m still waiting to hear from director and confirm his appearance at the hearing.”

In an interview prior to the Mueller announcement, Chaffetz said Republicans had texted to thank him Tuesday night after he requested Comey’s notes from the FBI.

Most are from competitive districts and fear how Trump’s actions may play in the midterm elections, he said.

“I had a number of members send me a personal text saying, ‘Thank you,’ ‘good job,’ ‘keep it up,’ ‘glad we’re out there, not ducking this,’” he said.

The appointment took place against the backdrop of mounting controversy for the Trump White House. The president and his aides are now grappling with the repercussions of Comey’s firing, as well as the revelation Trump disclosed highly classified information to Russian officials and pressured Comey to drop the Flynn investigation.

Senate Majority Leader Mitch McConnell (R-Ky.) had broken his silence on the Comey affair Wednesday to say that lawmakers “need to hear from him as soon as possible.”

“I think we need to hear from him about whatever he has to say about the events of recent days, as soon as possible, before the Senate Intelligence Committee, in public,” McConnell said in an interview with the Wall Street Journal.

Meanwhile, leaders of the Senate Intelligence and Judiciary committees asked the FBI to hand over Comey’s notes about his communications with the White House and senior Justice Department officials related to the Russia investigation.

Judiciary Committee leaders also asked the White House to provide any records of interactions between Trump officials and Comey.

A handful of Republican lawmakers from swing districts voiced strong praise for the Justice Department’s decision.

“It is evidence that this administration is taking the Russia probe seriously,” Rep. Carlos Curbelo (R-Fla.) told MSNBC.

“Right thing to do and the right choice,” tweeted Rep. Barbara Comstock (R-Va.), who worked at the Justice Department while Mueller was FBI director.

Other Republicans were less openly enthusiastic. “I’m fine with it,” said Rep. Bill Flores (R-Tex.), who was among those who had resisted an independent prosecutor.

Rep. Mark Meadows (R-N.C.), chairman of the generally pro-Trump House Freedom Caucus, called it “a prudent move, and it certainly means that the administration is taking it seriously.”

But he suggested Mueller “comes with more credibility on the Democrat side than on the Republican side,” a remark he said was based on “sworn testimony that he’s given here on Capitol Hill since I’ve been here.”

“I can’t say it’s good, bad or indifferent. This goes in the ‘is-what-it-is’ right now,” said Rep. Chris Collins (R-N.Y.), a stalwart Trump supporter.

“This is a development, it’s done, then let’s move forward,” said Rep. Tom MacArthur (R-N.J.). “The key is, whether it’s through a special prosecutor or the FBI investigation or the House or the Senate investigations, we have to get to the truth about what Russia did, and we have to make sure that they pay a price for that, and that no country ever thinks that they want to mess with one of our elections ever again.”

Democrats were much more effusive, though some insisted the Mueller appointment should only be a “first step.”

“Director Mueller will still be in the chain of command under the Trump-appointed leadership of the Justice Department. He cannot take the place of a truly independent, outside commission that is completely free from the Trump administration’s meddling,” House Minority Leader Nancy Pelosi (D-Calif.) said in a statement.

Rep. Elijah E. Cummings (Md.), the ranking Democrat on the oversight committee, said Mueller’s appointment might have “taken some of the pressure off” Republicans to get on board with an independent commission.

“But let’s be clear,” he added. “The Republicans cannot afford to stand on the sidelines and allow anybody to do anything to be above the law — none of us can.”

Cummings guessed that Mueller’s investigation would likely cover more ground.

“Clearly, all these investigations will overlap, but the one that Mr. Mueller will be overseeing will probably have the most significance in a lot of ways because, number one, they will have the full weight of the federal government, and the Justice Department, and if charges are appropriate, he’ll be able to bring them,” he said.

“And they I’m sure will have the resources to go wherever the evidence may lead,” he added.

Republicans have been more candid in describing their concerns about Trump over the last two days.

On Tuesday night, Sen. John McCain (R-Ariz.) compared the current situation to the Watergate scandal while speaking at an International Republican Institute dinner.

“We’ve seen this movie before. I think it’s reaching the point where it’s of Watergate size and scale and a couple of other scandals that you and I have seen,” McCain told Bob Schieffer of CBS News.

“There’s a lot here that’s really scary,” Sen. Ben Sasse (R-Neb.) said Wednesday morning in an interview with conservative radio host Hugh Hewitt. “It’s obviously inappropriate for any president to be trying to interfere with an investigation.”

Sen. Patrick J. Toomey (R-Pa.) said he believes “changes are needed at the White House” to such a degree that he is calling for a Democrat to replace Comey as head of the FBI.

Republican leaders had managed to fend off calls for a special prosecutor or independent commission to take over the Russia investigations. But signs of disagreement were increasing within the party.

Rep. Charlie Dent (R-Pa.), co-chairman of the moderate Tuesday Group, said the collective political fallout from the past week “will make it difficult” for Republicans to resist backing some sort of independent investigative body.

“We may have to move in that direction,” Dent said Wednesday at a forum moderated by Center Forward, a moderate Democratic organization.

Rep. Justin Amash (R-Mich.), one of two House Republicans to endorse an independent investigation of the Comey matter, joined Rep. Carlos Curbelo (R-Fla.) in saying that if the details reported this week are true, they could be grounds for impeaching Trump.

Ryan was careful to strike an evenhanded tone earlier Wednesday, saying congressional committees would continue to conduct oversight “regardless of what party is in the White House” but seeming to dismiss some concerns that have arisen in the wake of news about a memo by Comey suggesting that Trump had pressured him to drop the Flynn investigation.

Ryan also questioned why Comey didn’t “take action” after his meeting with Trump.

“There’s clearly a lot of politics being played here,” Ryan said. “It is obvious there are some people out there who want to harm the president.”

Carol D. Leonnig, Ed O’Keefe, Amber Phillips, Kelsey Snell, Sean Sullivan and David Weigel contributed to this report.