Senate Republicans argue House and Senate intelligence committees' investigations are continuing to proceed with bipartisan support, and that that they should be the primary vehicles for the investigation.
"I don't think we're there yet," Arizona Sen. Jeff Flake said of a special prosecutor.
A special prosecutor would be appointed in place of the current FBI investigation into ties between the Trump campaign and Russia, while an independent commission would replace the congressional investigations into the matter.
Sen. Richard Shelby, an Alabama Republican, said the Senate should give the intelligence committee time to complete its investigation before considering additional steps.
"A special prosecutor generally is far-ranging and never stops," Shelby said. "It goes everywhere and generally there's not much discipline to them."
Sen. Lisa Murkowski of Alaska was the first Republican senator on Wednesday to suggest a special prosecutor was needed to investigate the Russia allegations.
"It's imperative that we — Congress, the FBI, the administration — work to restore the public's trust," she said in a statement. "In order to gain the credibility, it may be that we need to look to an independent commission or special prosecutor."
Rep. Adam Kinzinger said he was open to a special prosecutor
, a shift from his comments earlier this year.
"It is time we look at the idea of an independent commission or special prosecutor," the Illinois Republican told CNN's Alisyn Camerota on "New Day.
And Rep. Mike Simpson, an Idaho Republican, also endorsed an independent commission for the Russia investigation, though he made the distinction that he did not support appointing a special prosecutor. He argued that the congressional investigations would be tainted by partisanship.
"Nobody's going to believe them," Simpson told reporters. "That's unfortunately just the way it is because it got so partisan."
Rep. Walter Jones, a North Carolina Republican, has also signed on to Democrat efforts to create an independent commission.
Several committees in Congress were quickly moving to address the Comey memo story Wednesday. The Senate intelligence committee invited Comey to testify and sought his memos, while the Senate judiciary committee requested the FBI memos as well as any possible tapes from the White House in response to Trump's tweet last week suggesting he had taped conversations with Comey.
And House Oversight and Government Reform Chairman Jason Chaffetz announced he was inviting Comey to testify before his committee next Wednesday, though the committee has yet to make contact with the former FBI director.
House Democrats also sought to ramp up pressure on Republicans by pushing for a discharge petition to force a vote on creating an independent commission.
Republicans on the intelligence panels defended their ability to carry out their investigations.
Sen. Susan Collins of Maine, a Senate intelligence committee member, said on CNN's "New Day" she did not support a special prosecutor for the investigation.
"I am confident that we will do a good job," Collins said. "I do think it would help if we brought in an experienced former prosecutor or an experienced investigator, and I have made that recommendation to both the chairman and the vice chairman."
Other Republicans are also sticking by the intelligence committees, saying they weren't confident that an independent commission or special prosecutor was a better option.
Sen. John McCain has long called for a select committee to investigate Russia, but the Arizona Republican does not back a special prosecutor.
"The problem with a special prosecutor is we've had mixed results in the past," McCain said.
Sen. Pat Toomey, a Pennsylvania Republican, pointed to bipartisan agreement thus far in the Senate intelligence investigation, although the House's probe has run into partisan problems.
"I still have a lot of confidence in the Senate intelligence committee," Toomey said. "There's bipartisan leadership that have both very publicly committed to getting this job done."