LOS ANGELES — Mayor Bloomberg’s toe-testing of the national political waters rapidly turned into a full-scale plunge yesterday as his potential presidential bid won public votes of confidence from two powerful Californians, the mayor of Los Angeles, Antonio Villaraigosa, and the local police chief, William Bratton.

The near-endorsements from Messrs. Villaraigosa and Bratton came as Mr. Bloomberg joined them at a Los Angeles high school for an event showcasing efforts at education reform and reducing crime near troubled schools.

Asked about the possibility of a presidential campaign by Mr. Bloomberg, Mr. Villaraigosa was effusive.

“Look, he is a great mayor,” Mr. Villaraigosa said. “He’s the chief executive of the largest city in the United States of America, which, along with Los Angeles, are the two principal centers of hope and aspiration in America. I say, if he wants to throw his hat in the ring, so be it.”

Speaking to reporters after the meeting broke up, Mr. Bratton, who served as New York police commissioner from 1994 to 1996, touted Mr. Bloomberg’s record and said he would make a formidable presidential candidate.

“I think he would be adequately prepared to assume the responsibilities of president. As to whether he’d want the aggravation of it, after New York, he might not want any more,” Mr. Bratton said.

Asked whether he would vote for Mr. Bloomberg, Mr. Bratton said without hesitation that he would.

For his part, Mr. Bloomberg said yesterday that he was not wavering from his past public statements dismissing the notion of a race for the White House. He attempted to deflect the questions and comments by offering an unprompted suggestion that Mr. Villaraigosa is presidential material.

“If the Democratic Party is looking for a candidate for president in 2008, I think here’s somebody who clearly is a demonstrated leader,” a smirking Mr. Bloomberg said as he stood alongside the Los Angeles mayor. “I can’t at this point rush out to endorse you yet. I can’t go quite that far yet.”

Despite Mr. Bloomberg’s good-natured disavowals of interest, his political aides and supporters are actively promoting the idea of an independent bid for the White House. There also have been persistent reports that Mr. Bloomberg has had serious discussions about the possibility with prominent donors and political strategists.

The visit to Los Angeles was intended to highlight the successes Mr. Bloomberg has had since taking greater control of the New York City schools. Mr. Villaraigosa recently won permission from the state Legislature in Sacramento to take a central role in improving Los Angeles area schools.

Today, Mr. Bloomberg is scheduled to engage in overtly political activity, attending two fund-raisers in Northern California for Governor Schwarzenegger, a Republican who seems to be on the verge of an easy re-election this fall. The two men also are expected to visit a fuel cell facility to underscore their commitment to combating climate change.

A leading political analyst in California, John Pitney Jr. of Claremont McKenna College, said any independent candidacy for the White House is an uphill battle, but that Mr. Bloomberg would be better positioned than others who have tried.

“He could make a very serious go of it, particularly if the Republicans and Democrats nominate polarizing figures as their presidential candidates,” Mr. Pitney said. “Recent history suggests that’s a good chance. There would be space for a third candidate, given a candidate willing to spend a lot of money.”

Mr. Pitney said Mr. Bloomberg’s liberal social views and moderate fiscal policies could have wide appeal in California. “Kind of like Arnold without the steroids,” the professor said.

While Mr. Schwarzenegger is embracing the centrist Republican mayor from New York, the former action film star is expected to steer clear of President Bush when he makes a visit to the Golden State next month to campaign for congressional candidates. California Democrats have tried, with mixed success, to sink Mr. Schwarzenegger’s approval ratings by tying him to Mr. Bush, who is not popular here.

Asked why Mr. Schwarzenegger was unlikely to meet up with the president on his upcoming trip, Mr. Pitney chortled and said, “Scheduling conflict. Scheduling conflict.”

One challenge Mr. Bloomberg would face in any presidential bid is that he is largely unknown in the West.

Mr. Villaraigosa took some steps toward remedying that yesterday. Standing in front of no fewer than 10 television cameras, he sang Mr. Bloomberg’s praises, calling him one of the best mayors in the country.

He also repeated his remarks in Spanish for the benefit of California’s booming Latino population.

At several points, Mr. Blooomberg gamely joined in, referring to himself as a “gringo.”

Mr. Bratton was appointed police commissioner in New York by another potential presidential candidate for 2008, Mayor Giuliani.

The veteran police official, who reportedly left in a tiff with Mr. Giuliani, was a bit more reserved when asked to size up Mr. Giuliani’s chances for the White House. “If he does get into the race, he’s going to be a very strong candidate, I think, a viable candidate,” Mr. Bratton said. Mr. Giuliani, who is expected to run for the Republican nomination, could have trouble with conservatives in his party, the police chief said.

Asked if he would vote for Mr. Giuliani, Mr. Bratton said, “It would all come down to who was in the race.”