New York Mayor Michael Bloomberg’s potential independent bid for president depends largely on whether the major party candidates embrace the political center and eschew the divisiveness prevalent in Washington, said Democrats and Republicans who participated in a summit Monday with the mayor.

The bipartisan gathering attracted former senators, onetime governors and a current lawmaker. But the main draw for the media, students and political junkies at the University of Oklahoma was Bloomberg, the multibillionaire businessman whose change in party affiliation last summer to independent captured front-page headlines.

Meanwhile, Sen. Chuck Hagel, R-Neb., who attended the forum and who has been widely mentioned as a running mate for Bloomberg, indicated his GOP credentials may not be permanent.

“As of right now, I’m a Republican,” Hagel said Monday, “and then we’ll see what the world looks like.”

During Monday’s gathering, Hagel focused on interconnection of the environment, energy and the economy, both at home and globally.

“Every one of us in this group this morning believes there are opportunities to turn things around for our country, our future, our children, the world,” he said.

Today’s leaders need to recognize the world is “more combustible and interconnected” than it once was, he said, and that issues facing the country also are interconnected.

Bloomberg has repeatedly denied he’s a candidate, but he has the wealth to launch a third-party bid, and talk of a candidacy has grown louder.

The bipartisan summit even stole a bit of the spotlight from the candidates in New Hampshire, coming on the eve of the first-in-the-nation primary.

“People have stopped working together, government is dysfunctional, there’s no collaborating and congeniality,” Bloomberg said to applause from the crowd.

Participants at the gathering who spent time alone with Bloomberg said he appears genuinely curious about running, but remains far from committed.

“I don’t really think the mayor wants to run — does that mean the mayor would never run if he still views the system as failing?” said former Democratic Sen. David Boren of Oklahoma, one of the meeting’s organizers, after the event. “I think he’s a good American, and I don’t think he would close the door on it if he thought it was his duty.”

The other leader of the summit, former Democratic Sen. Sam Nunn of Georgia, said the chances of a third-party bid have been dramatically altered by Democrat Barack Obama’s victory in Iowa and his embrace of bipartisan unity, combined with other candidates’ moves toward the center.

“It’s changed the calculation anybody would make in terms of whether they were going to run,” Nunn said after the forum.

Obama, during his victory speech in Iowa, told supporters: “You came together as Democrats, Republicans and independents, to stand up and say that we are one nation. … You said the time has come to move beyond the bitterness and pettiness and anger that’s consumed Washington.”

The Republican winner in Iowa, Mike Huckabee, also referred to a desire for bipartisan unity.

What Americans want, he said in his speech, is for their president “to bring this country back together, to make Americans, once again, more proud to be Americans than just to be Democrats or Republicans, to be more concerned about going up instead of just going to the left or to the right.”

These sentiments are good signs, said some of the panelists in Oklahoma.

“I hope that all the candidates say to themselves, ‘The public is tired with the partisanship and the special interests, and if I’m going to get elected, I’ve got to stand up and say what I believe is the big issue, hold myself accountable,’” Bloomberg said. “And maybe you are seeing that.”

The group spent several hours Sunday night and Monday morning drafting a joint statement about the urgency of drawing the parties to work together in addressing issues such as health care, climate change, homeland security and the economy. It urged the presidential candidates to provide “clear descriptions of how they would establish a government of national unity,” and “specific strategies for reducing polarization and reaching bipartisan consensus.”

The forum included former Republican Sen. Bill Brock of Tennessee, former Defense Secretary William Cohen, former Democratic Sen. Bob Graham of Florida, former Republican Sen. John Danforth of Missouri, former Democratic Sen. Gary Hart of Colorado and former New Jersey Gov. Christine Todd Whitman.

Nunn and Boren repeatedly said they did not intend the meeting to be seen as building support for a Bloomberg candidacy. Several of those attending made it clear they were not interested in that storyline, and many said privately that the group was clearly divided on this topic.

Cohen, a Republican, said during the forum that he wanted to find consensus, “not to be here as a promoter for anybody’s candidacy or any party, but to serve as a catalyst for starting a deeper and more profound dialogue for what it takes to make this government of ours work.”

Some in the audience were skeptical about a Bloomberg candidacy.

“I don’t know anything about him, but that’s why we’re here,” said Pam Hughes, a 48-year-old law student and registered Republican from Norman. “Just because you can run New York City — sorry Rudy Giuliani — I don’t know if that qualifies you to run the country.”

Bloomberg kept a low profile and left without speaking with reporters.

The mayor has been entertaining presidential speculation for more than two years, but time is closing in. Deadlines for access to general election ballots are fast approaching.

The earliest deadline is Texas. Bloomberg would need to collect about 74,100 signatures by May 12 and can only begin the petitioning there March 5. A number of states follow with June deadlines, including Arizona, Colorado and North Carolina.