"I think we're in good shape. We're ahead in maybe 16, 18 of the 29 states that are coming up," the former New York mayor said. "This was the first one. I think it's one that, quite honestly, we didn't expect that we would win. And we didn't put a lot of resources into it. And now we'll move on to the others."
Giuliani holds an early lead in polls in Florida, which conducts its primary Jan. 29, and he hopes a strong showing here will offset poor results in early-voting states.
He said he thinks his early-state strategy will pay off "in that we've paid a lot of attention to states that some other candidates haven't paid much attention to."
"I think our message of being on offense against terrorism, having been tested by crisis, how to handle difficult problems, I think that message will succeed in a number of these primaries," he said.
"I congratulate Mike. I think he's got a really good victory there" in Iowa, Giuliani added.
He was interviewed on MSNBC and CNN.
Earlier, Giuliani spoke to a rally of mostly Cuban-Americans, asking them for their help, votes and support on Jan. 29, in the tradition of another election that turned on the Sunshine State.
"I know how good you are at that because I've seen you pull us through," Giuliani said. "Remember, it's Florida that saved this country for the Republican Party in 2000."
Giuliani is counting on winning the delegate-rich Sunshine State to offset poor showings in early states like Iowa and New Hampshire. Rivals Mitt Romney, Mike Huckabee and John McCain are focusing on those traditional states.
However, experts have questioned whether Giuliani's campaign can survive a series of early losses, as well as Florida's influence in the nomination process.
The Republican winner in Florida will get fewer delegates to the nominating convention because the state broke national party rules by holding the primary before Feb. 5.
Asked after the rally about his unconventional approach to the nomination, Giuliani said: "Everybody has their own strategy."
"We think this is the one that fits," he added.
Giuliani made no mention of his Republican competition during the rally, which a few hundred people attended. He did, however, take a shots at Hillary Rodham Clinton and her husband's administration.
Referring to her as the leading Democratic candidate, Giuliani paraphrased her approach to taxes like this: "We have to take things from you for the better good."
The crowd booed.
"I have a different philosophy," Giuliani said. "I want to give some things back to you for the common good."
Touting the anti-terrorism theme that defines his campaign, he called for increasing the size of the armed forces, saying the "terrorists' war on us" should be approached from a position of strength.
"We have to be on the offense," Giuliani said. "No defense.
We have to be on the offense."
Giuliani, who leads in polls among Floridians, said the Cuban-American community was an example for what good can come of transitioning to a democratic society.
"Look at what you've achieved in such a short period of time. Look what freedom can do," Giuliani said. "The same thing can happen in the Middle East."
