WOLFEBORO, N.H. — Appearing at a boisterous gathering in the heart of this town on Lake Winnipesaukee, which just happens to be the summer home of his Republican rival, Mitt Romney, Mayor Giuliani is declaring himself the only GOP presidential candidate capable of winning a nationwide race.

Mr. Giuliani’s afternoon appearance yesterday at a local ice cream shop, Bailey’s Bubble, drew more than 100 tourists and area residents, one of whom reported having spotted Mr. Romney, clad in shorts and a T-shirt, on his boat the day before. The informal event took on the feel of an old-time political rally when the former mayor climbed to a landing to address the crowd. He made his way through a buzzing group of gladhanders, well-wishers, and autograph seekers of all ages and bought a cup of toffee ice cream. Throughout a day of events in New Hampshire’s Lakes Region, Mr. Giuliani appeared upbeat and energetic. Until now, other candidates, including Mr. Romney, have concentrated more time and effort on building an organization in the Granite State, where the former Massachusetts governor currently leads in the polls.

As he made his way back into the crowd from the ice cream counter, Mr. Giuliani stopped to answer a question from The New York Sun about what message the Wolfeboro appearance sent to Mr. Romney.

“None, other than New Hampshire is real important to us,” Mr. Giuliani said, ice cream in hand. “We want to win in New Hampshire. We think we can win in New Hampshire.”

Mr. Giuliani turned around the presumption that his status as a “national candidate” will hurt him here.

“We also think I’m the candidate for the Republican Party who can win back a lot of the Northeast and a lot of the West. We have to be competitive in every state and I think I have the best chance of doing that,” he said. “Every poll shows that, and I think most people know that. We have to be able to win in New Hampshire. … We’ve got to have a 50-state campaign, and at this point I’m the only Republican candidate who can come close to having a 50-state campaign.”

He added that his personal profile as a former mayor of a major Northeastern city allowed him to appeal to voters seeking change: “We have to present a different face to the American people. We’ve got to have a different dynamic.”

While not unique for New Hampshire primary politics, the mayor’s trip through such towns as Meredith, Moultonborough, West Ossipee, and Wolfeboro was somewhat out of the ordinary. Typically, presidential candidates focus their efforts on the voterrich southern tier of the state, which includes such communities as Manchester, Salem, and Nashua, as well as the seacoast. July is high tourist season in New Hampshire, following the disappearance of the dreaded black flies, and Mr. Giuliani’s events drew his share of out-of-staters throughout the day, among them a family from Pennsylvania, a vacationer from Louisiana complaining about the humidity, and New Yorkers still moved by his leadership on September 11, 2001.

“It is true that this time of year, all over New Hampshire, there are a lot of tourists. It’s also true in the winter,” Mr. Giuliani said. “The benefit is you reach New Hampshire voters and you reach voters from North Carolina, South Carolina, New York, and Ohio. You’ve got to run in all those places, too.”

Sheila Skelley of Wolfeboro said Mr. Giuliani’s positive appearance in her town suggests that Mr. Romney “needs to do some campaigning right in this town.” A former chairman of New Hampshire’s Republican Party and the chairman of Mr. Giuliani’s campaign in the state, Wayne Semprini, called the day of events a success. He said he was thrilled to see the heavy turnout given the relatively short notice; organizers were notified of the event only on Saturday afternoon.

A New Hampshire spokesman for Mr. Romney’s campaign, Craig Stevens, said he had no comment on Mr. Giuliani’s appearance in Wolfeboro. “We’ll come back up Wednesday,” he said.