Ensign resigned last week. He is under an ethics investigation over claims he violated rules in the aftermath of an affair with Cynthia Hampton, the wife of former top aide Doug Hampton, whom he allegedly helped obtain a lucrative lobbying job.

The former senator cited the investigation in his resignation statement. At the time of Ensign's resignation, the committee leaders said the investigation would proceed anyway. 

The committee's jurisdiction in terms of punishment is limited to serving senators but it could forward any criminal findings to the Justice Department. The Justice Department dismissed a previous probe on Ensign late last year.

Senate Majority Leader Harry ReidHarry Mason ReidWATCH: There is no Trump-Russia collusion and the media should stop pushing this The demise of debate in Congress ‘North by Northwest,’ the Carter Page remake MORE (D-Nev.) told reporters last month that the ethics committee is obligated to report any criminal findings.

"I think they are obligated, as I understand it, to come up with a report, and once they come up with a report, they are also required by law, if there are any criminal violations that they see, they are obligated to refer that. It is not a matter of discretion, they are obligated as a matter of law to refer that to the Justice Department," he said.