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."

The group in Oklahoma 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 Democratic Sen. David Boren of Oklahoma, former Democratic Sen. Sam Nunn of Georgia and former New Jersey Gov. Christine Todd Whitman.

"We come together to appeal to all presidential candidates to tell us how they plan to bring us together: Hear our plea, bring us together," Boren said.

Asked what he would do if the candidates did not respond, Bloomberg demurred.

"I think all the members of the panel are optimistic that the candidates will listen to us and will understand that there is a deep need in this country and a deep desire among the electorate to have the candidates face the issues," he said.

The billionaire mayor, who is in his second term, says publicly that he will not run, but his denials have weakened as his aides more boldly explore a potential candidacy.

The mayor has been entertaining presidential speculation for more than two years, but time is closing in — he needs to make a decision within about the next several months in order to begin the exhaustive and complicated process of collecting signatures to get on the ballot, a process that differs state by state.

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