Paul's comments are a break with top Senate Republicans who signaled on Tuesday that they expect the Senate Intelligence Committee will likely look into Flynn's calls as part of its ongoing investigation about Russia's involvement in the White House race. Paul is on the Foreign Relations Committee.

Senate Majority Leader(R-Ky.) noted that the Intelligence Committee has "broad jurisdiction" on its investigation and said it's "highly likely" the panel would want to probe the incident.

"We have standing committees that have all the appropriate clearances that can do an investigation," he said.

Democrats are doubling own on their push for a special committee or independent commission to be formed to probe Flynn as well as broader ties between the Trump team and Russia.

Flynn wrote in his resignation letter that he "inadvertently briefed the Vice President Elect and others with incomplete information regarding my phone calls with the Russian Ambassador" because of the "fast pace of events."