(CNSNews.com) – In a statement issued Wednesday after the Justice Department announced that former FBI Director Robert Mueller III would take over the FBI investigation of Russian efforts to influence the 2016 presidential election (“and related matters”), some Democrats applauded, but others called Mueller’s appointment as special counsel “a first step.”

They want a bipartisan, independent commission to do the investigation.

“A special prosecutor is the first step, but it cannot be the last,” House Minority Leader Nancy Pelosi (D-Calif.) said in a written statement.

She continued:

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.  A special prosecutor does not negate the need for vigorous Congressional investigations either.

The question also remains: will Mueller’s investigation include President Trump’s attempt to intervene in the investigation of Michael Flynn?  The American people have a right to the truth, free from the Trump Justice Department’s efforts to silence it.

On the positive side, Pelosi called Mueller “a respected public servant of the highest integrity.”

She also said Democrats are “pleased” the Justice Department “has answered Congressional Democrats’ calls for a special prosecutor,” and she said the Trump administration must ensure Mueller “will have the resources and independence he needs to execute this critical investigation.”

Senate Minority leader Chuck Schumer (D-N.Y.) tweeted: “A special counsel is very much needed in this situation and Deputy Attorney General Rosenstein has done the right thing.”

Rosenstein – heavily criticized by Democrats for his role in the firing of FBI Director James Comey – said he decided “it is in the public interest” for him to appoint a special counsel to look into all things Russia and Trump.

“My decision is not a finding that crimes have been committed or that any prosecution is warranted,” Rosenstein said. “I have made no such determination.

“What I have determined is that based upon the unique circumstances, the public interest requires me to place this investigation under the authority of a person who exercises a degree of independence from the normal chain of command.”

Mueller will resign from his private law firm to avoid any conflicts of interest with firm clients or attorneys.

Democrat National Committee Chairman Tom Perez said the Justice Department’s decision to appoint a special prosecutor “underscores the seriousness of the Russia investigation.”

“Despite the best efforts of Donald Trump and Congressional Republicans to hide the truth, millions of Americans have raised their voices in an effort to protect our democracy. But this fight isn’t over,” Perez continued. “President Trump has already made it his mission to end this investigation. That’s why we must remain vigilant against any attempt to interfere with justice. Republicans should listen to the American people and join Democrats in creating an independent commission.”

On the Republican side, Sen. Mitch McConnell (R-Ky.) did not support Democrat calls for an independent commission or special counsel, saying congressional committees should first reach their conclusions.

“The decision by the Deputy Attorney General to appoint former FBI Director Robert Mueller as a special counsel confirms that the investigation into Russian intervention into our election will continue, as stated last week by Acting FBI Director Andrew McCabe,” McConnell said in a statement.

“The Senate Select Committee on Intelligence will also continue its investigation into this matter,” he added.

House Speaker Paul Ryan (R-Wis.) sounded slightly more positive:

“My priority has been to ensure thorough and independent investigations are allowed to follow the facts wherever they may lead. That is what we’ve been doing here in the House.

“The addition of Robert Mueller as special counsel is consistent with this goal, and I welcome his role at the Department of Justice. The important ongoing bipartisan investigation in the House will also continue.”

Rep. Jason Chaffetz (R-Utah), the head of the House Oversight and Government Reform Committee, said he doesn’t think there is any need so far for a special prosecutor, but if there is going to be one, “it doesn’t get any better than Robert Mueller.”

“His credentials are impeccable,” Chaffetz told Fox News’s Tucker Carlson Wednesday night. “He served in the Bush administration, the Obama administration. No, he is unassailable in terms of his credentials, his background…he’s in the latter part of his career, he has nothing to prove, he’s been silent politically.”

But still, Chaffetz questioned the need to appoint a special prosecutor:

“I have not seen any evidence of actual collusion. Where is the actual crime that they think they need a special prosecutor to prosecute? I just – I haven’t seen it. There’s been a lot of flailing, but that flailing started before January 20th.”

Chaffetz has said he will subpoena notes reportedly taken by Comey following a conversation where President Trump asked Comey to drop the federal investigation into Michael Flynn, according to The New York Times.