SAN FRANCISCO — Governor Schwarzenegger of California is adding his voice to those urging Mayor Bloomberg to make a race for the White House in 2008.

“I would encourage him to run,” Mr. Schwarzenegger told Newsweek in an interview late last week. “The more the better. Competition creates performance.”

An aide to the governor confirmed the quote, but warned that it should not be viewed as an endorsement.

A spokesman for Mr. Bloomberg said the mayor was flattered by the governor’s remarks but is not seeking higher office.

“Mayor Bloomberg admires how much Governor Schwarzenegger has been able to accomplish in California by working across party lines and thinking outside the box,” the spokesman, Stuart Loeser, said in an e-mailed statement. “The Mayor appreciates the Governor’s kind words, but is not running for President.”

Mr. Bloomberg paid a visit to California in September, during which the movie star-turned-governor sang Mr. Bloomberg’s praises as a get-it-done leader capable of rising above the political fray. “He’s my soul mate. He’s the man,” Mr. Schwarzenegger gushed.

However, Mr. Schwarzenegger also enjoys friendly ties with other potential presidential contenders, including Senator McCain of Arizona and Mayor Giuliani.

The comment urging Mr. Bloomberg to run came during an interview where the governor also touted the possibility of moving California’s presidential primary contests to February from the presently scheduled date in June. He said he hoped such a change would give the nation’s most populous state more of a chance to affect the outcome of the primaries. “We don’t want to sit back and let this whole thing go by and have California not be a player,” the governor told Newsweek. He complained that presidential hopefuls have generally overlooked California’s voters, while “sucking us dry for money.”

A Republican political consultant based in California, Allan Hoffenblum, said Mr. Schwarzenegger may believe giving the Golden State a greater voice in the process would produce more moderate candidates. “Maybe Arnold thinks Bloomberg and Giuliani, his centrist candidates, would do well,” Mr. Hoffenblum said. Most speculation about a presidential bid by Mr. Bloomberg has focused on the possibility that he might mount an independent candidacy outside the main political parties, but Mr. Hoffenblum said the mayor could still run as a moderate within the Republican Party.

Others said it was far from clear whether moving up the California primary would help moderate Republican candidates. A political analyst at the University of California at Los Angeles, Sherry Bebitch Jeffe, noted that while California voters tend to be liberal, the most active members of the state’s Republican Party are quite conservative. “The Republican base here is not as moderate as the general electorate,” she said.

A longtime observer of the California political scene, John Pitney Jr. of Claremont-McKenna College, said moving the primary might be a logical second choice for Mr. Schwarzenegger, who is barred from seeking the presidency because he was born in Austria and later gained American citizenship.

“If you can’t be the king, you can be the kingmaker. Schwarzenegger can’t be president but he can put himself in the position of making candidates kiss the gubernatorial ring,” Mr. Pitney said. “A February primary puts Arnold in the center of the action, which is where he loves to be.”

Analysts said an early date for California’s primary could have the effect of boosting well-financed, well-known candidates such as Senators McCain and Clinton, while making it nearly impossible for other candidates to mount serious bids. “If California’s moved up very early, that means the invisible primary will be brutal,” Mr. Pitney said, referring to the contest for donations and endorsements that takes place before the first vote is cast.

It was not immediately clear yesterday how national leaders of the Democratic and Republican parties would react to a California primary in February. The possibility of upsetting or even crowding the status of Iowa as the first caucus state and New Hampshire as the first primary state has caused upheavals for Democrats. In a bid to increase diversity, South Carolina and Nevada were moved up on the calendar, but both states are dwarfed by California’s estimated 37.4 million population.

A North Carolina congressman who co-chaired a Democratic Party committee tinkering with the calendar, David Price, said California can move its primary to as early as February 5 without running afoul of the letter of the party rules. However, he made clear he is not a fan of the idea. “It would go against the thrust of the discussion of trying to pace the contests out a little more and especially have some of the big states going later,” Mr. Price told The New York Sun.