Sen. John Ensign issued a "heartfelt" apology to his Republican colleagues Tuesday for the extramarital affair he publicly confessed to in a news conference last week.

In a private meeting with other GOP senators, Ensign, R-Nev., said he was sorry for any negative ramifications his affair might have had on the party, according to sources present at the meeting.

Senate GOP Leader Mitch McConnell told reporters afterward that Ensign "spoke to our conference, apologized and said he was going to do his job."

"He was very, very sincere -- very heartfelt in what he said," Sen. Bob Corker, R-Tenn., said of the two-minute apology.

Sen. Mel Martinez, R-Fla., described the Nevada senator as "very contrite" in his apology, and said members were moved by the speech.

Ensign, a leading Republican mentioned as a potential presidential candidate, admitted to having an extramarital affair in 2008 with a woman who was a member of his campaign staff.

"Last year I had an affair. I violated the vows of my marriage," Ensign said at a brief news conference last week in Nevada. "It is the worst thing I have ever done in my life. If there was ever anything in my life that I could take back, this would be it."

The woman was later identified as 46-year-old Cindy Hampton, a former campaign treasurer for two committees connected to him. Hampton's husband, Doug, had served as an administrative assistant on Ensign's Senate staff.

Ensign spokesman Tory Mazzola has claimed Hampton's husband made "exorbitant demands for cash and other financial benefits" through an attorney within the past month -- a charge the Hamptons have denied.

Ensign, meanwhile, has quietly returned to work as questions continue to linger over the affair -- and his reason for publicly admitting to it. Ensign has said he intends to remain in the Senate, though he resigned as head of the Republican Policy Committee, the fourth-ranking spot in the leadership.

FOX News' Trish Turner and The Associated Press contributed to this report.