The major party presidential candidates might be hoping to charge into the New Hampshire primary with momentum from the Iowa caucuses this week, but a potential rival, Mayor Bloomberg, is aiming to slow them down.

On the eve of next Tuesday’s New Hampshire primary, Mr. Bloomberg will meet in Oklahoma with a group of politicians who consider themselves like-minded nonpartisans — a confab described as a warning shot to the Republican and Democratic candidates.

“It is a message to the two parties: Please rise to the occasion,” a former Democratic senator, David Boren, said. “If you don’t, there is always a possibility out there of an independent.”

Some observers say this threat from Bloomberg supporters — and the billionaire mayor himself — is the latest sign from the former businessman that he is considering entering the race.

“They want the major party candidates to promise not to be partisan or they won’t be happy? Come on — it’s a gesture, it’s a show,” the director of the Quinnipiac University Polling Institute, Maurice Carroll, said. “It’s an event to get attention and put Bloomberg front and center, where he can stay if he feels like it.”

Mr. Bloomberg, though, continued to publicly shrug off suggestions that he’d run for office. During an interview in Times Square on New Year’s Eve, he said that the forum was intended to seek an independent approach to politics and that he and others attending were sick of partisan politics.

“I’m not running for president,” he told the NY1 cable news station. “What I am trying to do is help us get an independent approach to government.”

The first stirs of Bloomberg presidential speculation came about two years ago when his political adviser, Kevin Sheekey, began floating the concept.

The idea twitched for months but mostly snowballed throughout 2007, gaining speed last June when he left the Republican party, declared himself an independent and began promoting himself around the country and on his relaunched personal Web site.

If he and his billions were to get into the race, advisers have said it wouldn’t happen until the two major party nominees are known. At that point, the Bloomberg camp would assess how his message of a centrist Democrat-turned-Republican-turned-independent would play against those candidates.

It remains unclear, however, how the centrist label would stick to someone who supports gay marriage and abortion rights, has sued out-of-state gun dealers as part of his national gun-control crusade, and has not been afraid to raise taxes and fees amid a budget crunch.

For now, Mr. Bloomberg sticks to a general message that partisan gridlock is choking the nation while he ramps up the winks and nods to keep reporters interested and remind the public that the field of candidates is by no means settled.

Mr. Bloomberg, who is usually known to demur when asked about the latest campaign rumor, made the rare move of publicly acknowledging his interests last week when responding to questions about a New York Post story that said advisers were reaching out to potential campaign consultants.

“Do I have advisers on lots of things? Sure. I know people — if I was going to run, I know exactly who to go to,” he said.

Next week, he’s going to the Oklahoma gathering, where he will sit down with friends like Senator Hagel, who has been mentioned as a potential Bloomberg running mate. In addition to Mr. Boren, other attendees include a former Republican senator, Bill Brock of Tennessee, a former defense secretary, William Cohen, and a former presidential candidate and Democratic senator, Bob Graham of Florida.

Organizers said the group plans to release a “set of principles” for the declared candidates.

Not all of the attendees are embracing the idea that this is a step toward a Bloomberg campaign.

Mr. Graham, who ran for the 2004 Democratic nomination, said that the meeting “is not a third-party effort” and said he didn’t think an independent candidate could get elected.

“Frankly, what I think is best for the country is to have a strong viable two-party system,” he said. “We have enough problems getting consensus with the two parties — our goal is to make suggestions on how to make the current system work.”

Mr. Cohen, speaking Sunday on CNN, seemed to be on the same page.

“I’m not interested in backing candidates,” he said. “I’m interested in being a catalyst to examine the issues that I think need to be focused upon.”