Hundreds of donors turned out for a Midtown presidential fund-raiser for Mayor Giuliani last night in what he called “a good start”to his exploration of a campaign for the Republican presidential nomination.

Officially, Mr. Giuliani’s camp said it was pleased with the showing for the former mayor’s first fund-raiser since he formed a presidential exploratory committee last month. The $2,100-a-head benefit was closed to the press, but supporters put the number of attendees at more than 400, which could yield more than $800,000 in seed money for Mr. Giuliani’s committee.

Mr. Giuliani spoke for about 20 minutes at the event, attendees said, touching on lessons that he had learned as mayor and saying the nation had to stay “on the offensive” fighting terrorists in Iraq and around the world.

Addressing reporters afterward, Mr. Giuliani had nothing but praise for one of his chief rivals for the Republican nomination, Senator McCain of Arizona, calling him “a fine man,” “a good friend,” and “a hero.”

But in a sign of the growing battle between the two men, Mr. McCain picked the day of Mr. Giuliani’s first fund-raiser to release a list of 57 prominent donors in the tristate region who have committed to his all-but-announced campaign, sending a signal to Mr. Giuliani on his home turf. The list includes Secretary of State Kissinger, the former chairman of the Lower Manhattan Development Corporation, John Whitehead, and Edward Cox. Mr. Giuliani expressed little concern about Mr. McCain’s move last night.

“John McCain is doing the same thing I’m doing. He’s exploring running for president,” he said. “I can understand why people would support him, and we’ll have a large number of people who support us, and then we’ll figure out who has the better chance.”

Mr. Giuliani also lauded Governor Romney of Massachusetts, noting that he and Mr. McCain were “probably the two most prominent” Republican hopefuls. One man he omitted was his former New York colleague, Governor Pataki, who has traveled extensively across the country to explore a presidential bid but has barely registered in most polls. Mr. Giuliani will decide formally on a presidential run “sometime next year,” he said, and he plans to travel to key states in the coming months. His exploratory committee yesterday unveiled its Web site, joinrudy2008.com, which features a photo of the former mayor, hands clasped, next to an early campaign slogan, “Proven Leadership.”

Among the attendees of last night’s fund-raiser at the Marriott Marquis were several longtime supporters of Mr. Giuliani and members of his administration, including a former fire and police commissioner, Howard Safir. The co-founder of Home Depot, Kenneth Langone, hosted the event.