Sen. Larry Craig, shown here in a 2005 photograph, is facing calls to leave the Senate.

Craig will leave office on September 30, the source said.

Earlier, several well-placed GOP sources in Washington and Idaho had said Craig was likely to resign soon.

GOP sources with knowledge of the situation told CNN's Dana Bash that the Republican National Committee was poised to take the extraordinary step of calling on Craig to resign but held off.

The RNC put the move on hold, the sources said, because top party leaders had received indications that Craig himself was preparing to step down.

Craig has been under pressure to quit since news surfaced this week that he was arrested in June at Minneapolis-St. Paul International Airport and later pleaded guilty to a disorderly conduct charge.

The arrest was made by an officer investigating reports of sexual behavior in an airport restroom.

In a post-arrest police recording released Thursday, Craig denied that he was trying to engage in lewd behavior in the airport bathroom and suggested he was entrapped by the arresting officer.

"I sit down to go to the bathroom, and you said our feet bumped," Craig told an officer. "I believe they did ... because I reached down and scooted over and the next thing I knew, under the bathroom divider comes a card that says 'police.' "

Craig said he was in the bathroom for its intended purpose and told the officers,"I am not gay. I don't do these kinds of things."

"You shouldn't be out to entrap people either," Craig said. Listen to the interview »

The officer accused Craig of lying during the contentious, eight-minute session, and said he would not take the senator to jail "as long as you're cooperative."

"I'm just disappointed in you, sir," the officer said. "I mean, people vote for you."

Craig spokesman Dan Whiting said Thursday the tape "speaks for itself."

The RNC held off its call for Craig to resign after it got word from Idaho Republicans that such a move could backfire, said GOP sources.

"Any official group saying he would have to resign would have been explosive," a GOP source told CNN. "Craig can't easily go if it appears he's been dictated to by the White House, the RNC, or any other party structure. It has to be his decision."

"He needed a grace period, a day with no action," said the GOP source. "He's gotten some breathing room, and that's helped."

Senate Minority Leader Mitch McConnell on Friday called Craig's conduct "unforgivable" and acknowledged that many in his caucus believe Craig should resign.