Top Republicans said Tuesday that it is likely Congress will launch a probe into former National Security Adviser Michael Flynn over his communications with Russia.

Senate Majority Leader Mitch McConnell told reporters it’s “highly likely” the Senate intelligence committee will investigate the retired army lieutenant general in the aftermath of his Monday resignation.

“I think the fundamental question for us is what is our involvement in it, and who ought to look at it,” the Kentucky Republican said. “And the intelligence committee is already looking at Russian involvement in our election.”

Speaking to reporters, the second-ranking Republican senator was blunt in his assessment of whether the Senate should investigate Flynn.

“Yes,” said Sen. John Cornyn of Texas.

He did not say, however, whether Flynn should testify before the Senate.

“I think it’s symbolic of somebody with a distinguished military career making a bad mistake,” Cornyn said.

Flynn resigned Monday after just three weeks on the job. The resignation came amid an uproar over talks he had had with a Russian diplomat, the content of which he didn’t fully disclose to the administration, and followed a Washington Post report that said the White House was warned that he could be vulnerable to blackmail.

Moreover, it was reported by The New York Times Tuesday that the FBI interviewed Flynn during his first days in the White House.

Sen. Roy Blunt, a Missouri Republican who is a member of the Senate Intelligence Committee, told a local St. Louis radio station that an investigation into Flynn “needs” to happen, and lawmakers need to speak with Flynn “very soon.”

“I think everybody 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.”

“What did he know?” Blunt continued. “What did he do? And is there any reason to believe that anybody knew that and didn’t take the kind of action they should have taken.”

Speaking to CNN Tuesday, Sen. Lindsey Graham of South Carolina joined calls for an investigation into Flynn’s correspondence with the Russian diplomat, saying he believes Congress “needs to be informed” of what was actually said in the conversations.

“And I want to know,” Graham said, “did Gen. Flynn do this by himself or was he directed by somebody to do it?”

Sen. Bob Corker, the Tennessee Republican who chairs the Foreign Relations Committee, spoke on multiple occasions Tuesday about the potential investigation, telling reporters “it wouldn’t be out of the question” for Flynn to testify before a Senate committee.

Corker said the Flynn resignation is “heightening the intensity” of the Senate’s wish to answer all of the questions circulating around Russia’s influence pre-and post-election, which have dogged Trump since he pulled off his improbable November victory over Democratic presidential nominee Hillary Clinton.

However, while it is illegal for unauthorised citizens of the US to negotiate with foreign governments, White House press secretary Sean Spicer insisted during Tuesday’s press briefing that no laws were broken. Spicer said the White House reviewed Flynn’s situation, and the national security adviser only resigned because his trust had “eroded” with the president.

Spicer’s comments jibed with prominent House Republicans who were not vocal in their requests to see Flynn investigated before its chamber of Congress.

Rep. Devin Nunes, a California Republican who chairs the House Intelligence Committee, instead focused on the stream of leaks from government officials to outlets such as The Post and The Times, saying his committee will investigate.

It echoed a Tuesday tweet from Trump in which the president said the “real story” was the “many illegal leaks.”

Rep. Jason Chaffetz, the Utah Republican who chairs the House Committee on Oversight and Government Reform, did not demand an investigation into Flynn from his committee, telling reporters “it’s taking care of itself.”

In a statement, Republican operative Kurt Bardella, who was formerly a senior adviser and spokesperson for the House Oversight Committee, said that if the first month of President Barack Obama’s administration had been anything like the first month of Trump’s, the committee would have been launching investigations “at a record pace.”

“When the tragedy of Benghazi unfolded and Susan Rice went on national television and misled the American people about what inspired the attack, Jason Chaffetz was rushing to every news camera he could find to call for investigation,” said Bardella, who worked for Chaffetz’s predecessor, Rep. Darrell Issa of California.

He added: “The litany of conflicts-of-interest and legitimate security questions that exist but have gone unanswered in the Trump Administration are more than enough grounds for numerous investigations and hearings … just as we did during the Obama Administration.”

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