The day after Americans in 24 states voted in presidential primaries, Mayor Bloomberg, a potential candidate for the White House, described his efforts to influence the national discussion from outside the race as an “experiment.”

“I’m trying,” he said. “I think I have an obligation to try to do it.” Mr. Bloomberg, who did not vote in Tuesday’s primary because he is an independent, said he is pleased the country may have something close to a national primary and said he hoped voters would base their decision about who to support “on rational reasons.”

He said he didn’t think the candidates were doing enough to talk about public education and foreign policy, but said Senator McCain and Michael Huckabee deserved some credit for presenting plans that address the country’s immigration policy.

The mayor has been paying a firm to conduct a nationwide voter analysis and has a plan in place to get on the ballot in all 50 states, his associates have said. He repeatedly denies that he is a candidate for president, which he reiterated yesterday.

But, he said he has the experience to speak out on national issues.

“New York City is the poster child for how you improve a public school system, New York City is the poster child for how you have a great police department,” he said, adding that “New York City has better election laws, our fatality rate for traffic and pedestrian accidents is a quarter of the rate in the rest of the country, so we have a lot of experience in all of this and we should be speaking out.”