President Obama asked staffers and note-takers to leave for a portion of his bipartisan meeting with Congressional leaders, a rare moment of privacy that the White House says was meant to give more a bit more intimate conversation and allow everyone to speak more candidly.

Those who were requested to step out included both White House AND Congressional staffers.

Adding to the unusual nature of the more-closed off part of the day, the president moved the group from the Roosevelt Room to a private dining room just off the Oval Office.

The more isolated portion lasted about 35 minutes and included President Obama, Vice President Biden along with Congressional Republican and Democratic leaders who attended the meeting. Obama even asked Treasury Secretary Tim Geithner, and Office of Management and Budget Director Jack Lew to leave, who were key to the discussing a tax cuts compromise.

The president didn't give many details on that portion of the meeting, but did reference it in his statement to the press after the gathering.

"And in a private meeting that I had without staff, without betraying any confidences, I was pleased to see several of my friends in the room say "let's try not to duplicate that, let's not try to work the Washington spin cycle" to suggest that somehow the other side is not being cooperative," Obama said.

Press Secretary Robert Gibbs said in Tuesday's briefing that the moment was rare, at least for a bipartisan meeting.

"I think it provides people with a candid -- they can be even more candid than they could be in a room full of people. And that's why the President would -- sought to do it. And, again, I think the President believed that both parts of the meeting were productive," said Gibbs.

Obama added that during that part, they did discuss a goal to move beyond the jabs that were a hallmark of the midterm election season.

"I think that there was a sincere effort on the part of everybody involved to actually commit to work together to try and deal with these problems. And they understand that these aren't times for us to be playing games," he said.

He noted that he had said in the open session in the beginning that there will be plenty of time for campaigning in the next election just two years away.

The president said he hopes to have more of these types of conversations with Congressional leaders and hinted to holding more meetings at Camp David, the presidential retreat in Maryland.

Tuesday's meeting was originally scheduled for a couple weeks ago, but was moved to do scheduling conflicts with Republican leaders.

Those in attendance for the nearly two-hour meeting included Senate Majority Leader Harry Reid, D-Nev., Sen. Minority Leader Mitch McConnell, R-Ky., Democratic Whip Sen. Dick Durbin, D-Ill., Republican Sen. Jon Kyl, R-Ariz., Republican Whip Rep. Eric Cantor, R-Va., House Majority Leader Rep. Steny Hoyer, D-Md. and House Speaker Nancy Pelosi, D-Calif.