"If your implication is that the White House wants this, I think that's wrong", said Senate judiciary chair Chuck Grassley Wednesday night.
Mr Robert Mueller, a highly respected former Federal Bureau of Investigation (FBI) chief, was appointed by Deputy Attorney-General Rod Rosenstein on Wednesday - reportedly with only a half-hour's notice given to the White House.
Senate Democratic Leader Chuck Schumer said Comey should still appear before congressional committees that have invited him to testify.
"There is no collusion between certainly myself and my campaign - but I can only speak for myself - and the Russians". Trump said in a tweet.
"Graham said that the creation of the special counsel will likely hamper congressional probes". "This is the single greatest witch-hunt of a politician in American history!"
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President Donald Trump has told graduates of the US Coast Guard Academy that no other politician has been treated more unfairly by the media.
Despite the president's furious reaction, some fellow Republicans welcomed Mr Mueller's appointment and expressed hopes it would restore some composure to a capital plunged in chaos.
Graham said congressional committees and subcommittees will now find it hard to subpoena the records of somebody like former National Security Adviser Michael Flynn or to call former FBI Director James Comey to testify: "If I were Mr. Mueller, I would jealously guard the witness pool", Graham said.
"We'll get rid of the smoke and see where the actual issues lie", said Sen.
On Thursday, Rosenstein informed the Senate in a closed-door session about Trump's controversial decision to dump Comey. And I think it's a very, very negative thing.
The same pattern was in evidence when he fired FBI Director James Comey last week then used a television interview to suggest he acted out of frustration with the FBI's Russian Federation probe - even though his team spent several days saying the ousting of the bureau's director had nothing to do with that issue. Trump himself had already contradicted that explanation, telling interviewers earlier that he had already made a decision to dismiss Comey.
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But it was not disclosed earlier how frequently he went incognito into cockpits of regular commercial flights. Fokker 70 was a narrow-body regional airliner, and now the monarch is being retrained to fly a Boeing 737.
He offered new justifications for his decision on Thursday, even while referring to the Rosenstein memo as "a very, very strong recommendation".
Mr Trump referred to Mr Comey's appearance at a recent Capitol Hill hearing, after which the Justice Department ended up having to amend part of his evidence regarding last year's probe of Hillary Clinton's email practices.
"That was a poor, poor performance", Trump said.
Instead of being a popular decision, the firing was met by a tsunami of criticism by Democrats because as FBI director, Comey oversaw the investigation of Russian meddling in the USA election and potential ties to Trump's campaign.
"There (were) no facts laid out as to why you would change that, but appointing a special counsel has created, I think, a dynamic for Congress that's going have to be leery of crossing into Mr. Mueller's lane because the possibility of a criminal investigation".
Former FBI director Mueller appointed as special counsel in Russian Federation investigation
John McCain, R-Ariz., said Trump would be making a mistake to start a rhetorical war with the new investigator. Trump said he was about to name a replacement for Comey, another move to settle the waters.
Senate intelligence Chairman Richard Burr, a North Carolina Republican, noted that Senate investigators were still pursuing former national security adviser Michael Flynn, even though they do not yet know how Flynn will respond to their subpoena for documents. "I hope that we don't inadvertently trip up or damage the independent investigation of the special counsel", he said.
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