The top Republican on the Senate Foreign Relations Committee is calling for a "fulsome" and timely investigation into the attempts by Russia to meddle in the 2016 presidential election, saying the need for such a probe is "heightened" in the wake of national security adviser Mike Flynn's resignation.

"I do think there needs to be a fulsome investigation [into] all angles relative to the nefarious activities that were taking place with Russia beginning in March, but even back before that time," Sen. Bob Corker, R-Tenn., told reporters Tuesday morning.

Corker said he hasn't reached a conclusion about the best way to ensure the probe is independent and timely, but he said there should be as many public hearings as possible while still protecting classified material.

"I know we've got to do that soon, and this heightens that, obviously," he said.

Corker said "there's mounting frustration about the pace" of existing congressional probes and that the American people deserve to have a thorough accounting of Russia's activities.

"So I'm open to looking at a way to make sure that all of us and the American people understand everything that's occurred relative to their nefarious activities and the relationships they had," he said.

Corker's remarks are the most aggressive calling for a stepped-up congressional response to investigating Russia's efforts to influence the presidential election after Flynn's forced resignation.

Democrats earlier Tuesday called for an independent, bipartisan commission to investigate Flynn's interactions with Russia, as well as Moscow's interference in the election.

Corker stopped short of endorsing such an idea, arguing that these types of blue-ribbon commissions often take years to produce findings and may not have access to all the classified materials that a congressional panel would.

Other top Republicans also said Congress needs to investigate Flynn. Sen. John Cornyn, the No. 2 Senate GOP leader, said Tuesday that the Congressional Committees with jurisdiction, including the Senate Intelligence panel, should investigate Flynn and the issues surrounding him regarding the Trump administration's ties to Russia.

Sen. Richard Burr, who chairs the Intelligence panel, has previously said his committee would look into the evidence of Russian hacking in an attempt to meddle in the presidential election. Burr told reporters Monday that he hasn't made a decision yet on whether Flynn should testify in the probe but stressed that there would be no public hearings.

"We plan to continue to do aggressive oversight in the committee privately – we don't do that in public," he said.

Sen. Roy Blunt, R-Mo., who also serves in the GOP leadership and on the Intelligence Committee, told a local radio station that an investigation "needs to" happen.

"I think everyone needs that investigation to happen," he said. "And the Senate Intelligence Committee, again that I serve on, has been given the principle responsibility to look into this, and I think that we should look into it exhaustively so that at the end of this process, nobody wonders whether there was a stone left unturned, and shouldn't reach conclusions before you have the information that you need to have to make those conclusions."

Sen. John McCain, R-Ariz., who chairs the Armed Services Committee, has already said his panel will investigate the evidence of Russian cyber-hacking during the election.

He told reporters Tuesday that it is "too soon" to say whether an outside commission should be formed or if the probe should be left to internal Congressional committees to continue to pursue.

After Flynn's resignation, McCain earlier Tuesday issued a scathing statement about the disarray in the national security apparatus under President Trump's leadership typified by Flynn's forced resignation.

Sen. Lindsey Graham, R-S.C., who launched his own Judiciary subcommittee probe of Russian meddling in the elections, wants to know if Flynn acted alone or at the direction of more senior officials or Trump himself.

"I think it's important for us to be informed about the phone call, did he do it by himself? Did he go rogue? Did someone suggest he call the Russians?" Graham said Tuesday. "I know we would be upset as Republicans if the Obama administration had done this…bottom line is, I want to know was there any legitimacy to the idea that Flynn could be compromised? I want to know if that's just all talk."

"I think the White House hopefully will work with Congress to get us the information we need. Time will tell," Graham said when asked if there should be an independent investigation.