On the eve of an Oklahoma conference of “independent” political figures from across the country, Mayor Bloomberg is using some of his harshest language to date to criticize presidential hopefuls from both parties, saying they are failing to address problems with health care, education, immigration, and foreign policy.

“I have not heard anybody that has said what they will really do when it comes to foreign policy. How they would rebuild the relationships that the country has around the world or used to have?” Mr. Bloomberg said yesterday during a press conference at City Hall, adding fuel to speculation about a presidential run of his own.

“Don’t say Bloomberg is criticizing A, B, or C on either side — it’s all of them,” he said.

“And I think that’s the frustration you see among a lot of independently minded people from both sides and the middle of the aisle, and that’s why I’m thrilled to be asked to participate in the conference in Oklahoma,” Mr. Bloomberg said.

During a television appearance on Monday, the mayor said he “will not run for president,” but yesterday he seemed to retreat from that strong denial, leaving the door open for a possible bid. “I’m not a candidate,” Mr. Bloomberg said yesterday, “but I am going to speak out.”

During a press conference at City Hall, Mr. Bloomberg fell short of promising he would finish his second term, saying: “My intention is to do that.”

Mr. Bloomberg said he is attending the Oklahoma conference to “find a way to take an independent approach to government” and to “find a way to get partisanship out of politics and get the special interests out.”

The meeting has fueled speculation that its participants, who include such prominent figures as Senator Hagel, a Republican, Senator Graham, a Democrat, a former defense secretary, William Cohen, and a former administrator of the Environmental Protection Agency, Christine Todd Whitman, might organize a third-party presidential run behind Mr. Bloomberg.