In a closed-door meeting, Ensign delivered what Tennessee Senator Bob Caucus said was "a heartfelt apology" to his colleagues, the Washington Post reports.
"He spoke at our conference, apologized and indicated that he was going to do his job," Senate Republican leader Mitch McConnell told reporters, according to the Associated Press.
The Nevada senator's apology was accepted by his GOP colleagues.
"He apologized and we welcomed him back," Sen. Robert Bennett told reporters.
Ensign admitted to having an affair with Cynthia Hampton last week and soon after resigned from his leadership role on the Republican Policy Committee.
Although his colleagues have accepted his apology, Fox News' Sean Hannity is calling on Ensign to resign from the Senate.
In response to a claim that he is defending Ensign, Hannity said, "My answer is, if you're going to be a family-values candidate and a family-values politician, and you don't live up to that, I think you should resign," Think Progress reports.
Ensign, a social conservative who harshly criticized Bill Clinton and Larry Craig for their personal scandals, dodged the media and declined to comment publicly today.