Secretary of State Rice gave her blessing yesterday to New York City’s Olympic bid as the city’s Olympic delegation prepared to make one last effort to sway members of the International Olympic Committee before the body votes next Wednesday.

Ms. Rice’s visit marked the first time in modern memory that a sitting secretary of state has visited New York’s City Hall. It was also the first time a top member of the Bush administration has attended a rally orchestrated by NYC2012, the city’s Olympic bid committee.

Ms. Rice met privately at City Hall with Mayor Bloomberg; the deputy mayor for economic development and rebuilding, Daniel Doctoroff; the president’s representative to NYC2012, Roland Betts; the city’s official 2012 delegation outfitter, Oscar de la Renta, and other Olympics officials at City Hall in the morning. Mr. Bloomberg said the private discussion was partly about the city’s bid, a “tiny bit” about the world, and mostly about sports.

In the early afternoon, Ms. Rice addressed hundreds of flag-waving New Yorkers at a “send-off” rally at City Hall Park.

“I think the chances are very good,” she told reporters. “I’ve been impressed with the way this city has dealt with all of the questions that have come up about the bid. … This city really does represent the best of America and the best of the world in a way that people come here and achieve from all over the world. I think it really does have a very, very good chance.”

Mr. Bloomberg said he was “thrilled” that Ms. Rice came to City Hall, the day before New York’s delegation flew off to Singapore, where the IOC will select one of five cities to host the 2012 Summer Games.

“We’re enormously grateful that somebody of Secretary Rice’s stature, somebody who is recognized around the world as representing the United States and the great parts of the United States, has come here today with the sole purpose of meeting with us and attending our Olympic rally,” the mayor said. He said he wished Ms. Rice could join him in Singapore but the city understands that she’ll be busy helping to run the country.

Although Ms. Rice said President Bush stands firmly behind New York’s Olympic bid, Mr. Bush will not attend the gathering in Singapore, as will the prime ministers, kings, or presidents of Spain, Russia, Britain, and France, the other four countries with cities in the running for the Olympics.

Instead, Mr. Bush will be featured via video in the city’s final presentation to the IOC, Ms. Rice said.

“You know what a sports fan he is,” she said of the former co-owner of the Texas Rangers baseball team. “He’s looking forward to having a chance to add his voice to this. My understanding is an American president has never gone to this session, and so it’s not unusual.”

She said Mr. Bush’s sending of Mr. Betts, a close friend since college, to represent him in Singapore shows his dedication to hosting the Games.

Mr. Betts, who was a partner of Mr. Bush’s in the front office of the Texas Rangers and is founder and chairman of Chelsea Piers, said “there is no bigger fan than President Bush” of the Olympics movement. He said the president had followed the ins and outs of the United States Olympic Committee selection process, as well as the “saga” surrounding New York’s Olympic stadium, which until this month was planned to be built on the far West Side of Manhattan. Now, if New York City is chosen as host city, the Olympic stadium would be an expanded version of a new Mets stadium in Queens.

Much of the city’s delegation is heading to Singapore today to begin, as the mayor put it, to “buttonhole” members of the IOC, talking to them about the intricate details of the city’s bid. The city will give one final presentation of its bid to the committee before the voting begins next week.

Mr. Doctoroff, who orchestrated the city’s bid, said that based on conversations with the 115 voting members of the IOC, he thinks the city has a good chance.

“I think there is a real recognition among those voters that New York offers something different,” he said. “We offer a different kind of city. We all know all five cities can host a very good Games. But what we offer is a different kind of athlete experience. We offer great opportunities for sports to grow, particularly in a market like the United States, where many of them are undeveloped. But most importantly, I think we offer an incredible message for the Olympic movement.”

Mr. Doctoroff added that the odds aren’t always good predictors of outcomes in the world of the Olympics.

“In seven of the last nine bidding competitions, it has been wrong, because what happens when they get into the room in a secret ballot is often very, very, very unpredictable,” the deputy mayor said. “I’m not guaranteeing victory. What I’m saying is that we have a lot of momentum. There is great enthusiasm among the members because of what we offer, and really, most importantly, what New York represents to the world.”