Mayor Michael R. Bloomberg of New York has remained coy about whether he plans to endorse a presidential candidate this year, even as Mitt Romney and President Obama aggressively court the billionaire media mogul.

The most that the mayor and his aides have said is that Mr. Bloomberg, who did not endorse in 2008, is carefully weighing his options this time around.

But during casual conversations at charity event a few days ago, Mr. Bloomberg was far chattier — and candid — about the subject, according to three people who overheard him.

Mr. Bloomberg said that he believed Mr. Romney would probably be better at running the country than Mr. Obama, according to two guests.

But Mr. Bloomberg said he could not support Mr. Romney because he disagreed with him on so many social issues, these two people said. The mayor mentioned two such issues: abortion rights and gun control.

As a result, Mr. Bloomberg said, he intended to remain neutral, said one guest.

The mayor’s office declined to comment on the conversation.

Mr. Bloomberg spoke about the election last Monday during the annual fund-raiser for the Mayor’s Fund to Advance New York City, a nonprofit with close ties to City Hall. The charity dinner was held on the roof of 200 Fifth Avenue, home of Eataly, the gourmet Italian market. (Among the guests were Mario Batali, the chef and Eataly partner, and Anna Wintour, the editor of Vogue.)

A guest at the dinner had asked the mayor for his feelings about the two candidates, prompting a lengthy reply, which was overheard by other guests. Two of those guests spoke on condition of anonymity, saying they feared upsetting the mayor by discussing a private discussion; a third was a reporter for The New York Times.

Guests described the mayor as relaxed and talkative, as he often can be at the evening events he attends several times a week.

Both Mr. Romney and Mr. Obama are vying for the political support of Mr. Bloomberg, whose name is all but synonymous with corporate-style management, Wall Street clout and nonpartisan politics.

Mr. Romney met with Mr. Bloomberg at the headquarters of the mayor’s philanthropic foundation on May 1. Over juice and coffee, the men discussed a wide range of policy issues.

A week earlier, the White House had invited Mr. Bloomberg for separate rounds of golf with two members of the Obama administration — Vice President Joseph R. Biden Jr. and Defense Secretary Leon E. Panetta.

After those outings became public, Mr. Bloomberg said he would “see down the road” about an endorsement. He offered this assessment of the candidates: “They’re very different, and they give the public a real choice. It’s hard to argue that you can’t tell the difference, if you will. They run the spectrum on lots of different issues.”