CONCORD, N.H. — Rudy Giuliani isn't convinced that any of the declared Republican presidential contenders can defeat President Barack Obama.

Until he is, Giuliani says he won't rule out a run of his own.

"These are a lot of qualified people," the former New York City mayor told The Associated Press on the eve of his fourth visit to New Hampshire this year. "Do they have a good chance of winning? I don't know the answer to that."

Giuliani, who acknowledges that his failed 2008 campaign was deeply flawed, has five public appearances scheduled during a two-day visit starting Thursday to the first-in-the-nation primary state. The stops include a luncheon with the Seacoast Federation of Republican Women in Portsmouth, a more intimate gathering at a private New Castle home with law enforcement officials and a gun-rights discussion at Manchester Harley Davidson.

It may sound like a candidate's schedule, but Giuliani backed away from an aide's recent comment that he would decide "very soon" whether to join the presidential field. He ruled out any decision before the end of July and said his timeline is late August or early September. He argued that he still has the drive to extend his political career.

"I have a tremendous fire for more public service," Giuliani, 67, said. "That's something that I feel sort of incomplete about."

Still, he doesn't sound eager to be considered even a potential candidate.

"I certainly haven't decided to get in. I don't think I would even describe myself as testing the waters. I'd say that I keep it open as a possibility," he said, adding he was going to New Hampshire at the invitation of local Republicans. "And it will give me a chance to gather more information and get a better feeling for it."

There's a general feeling among New Hampshire Republicans that Giuliani won't run. But if he does, GOP officials here say Giuliani would face tremendous hurdles, partly because many candidates have been building state organizations for months.

"It would be very daunting, particularly when you look at the campaign staffs that several of the candidates have. They've been here a while," state GOP Chairman Jack Kimball said. "But it really comes down to the voters and the passion that they feel for the person."

When it comes to Giuliani, there is evidence of lingering resentment from New Hampshire activists who supported him last time only to watch him employ a national strategy that largely ignored the Granite State, as well as early voting contests in Iowa, Michigan, Nevada and South Carolina. His strategy hinged on Florida, a state he ultimately finished third in before dropping out of the race completely.

He finished a disappointing fourth in New Hampshire last time. This year virtually every member of Giuliani's 2008 New Hampshire team is backing someone else.

That list is led by Doug Scamman, the former mayor's state chairman in 2008, who now is backing Romney and lent his Stratham farm for Romney's official announcement speech last month.

Giuliani doesn't think the damage is irreparable.

"They have a right to be resentful. I made a big mistake last time," he said. "I think people respond very, very well to somebody just saying they were wrong. I was wrong and will do it differently."

He may not be done apologizing.

"I've done that the last four times I was there," he said, laughing. "I keep apologizing. And I mean it. It's OK. I mean it."

Still, Michael Dennehy, a political consultant who previously led John McCain's presidential campaign here, and others say Giuliani is one of the few remaining potential candidates with the national profile to be a factor, even this late in the game.

"If you look strictly at the numbers, his image is very good" and he's well known, Dennehy said.

Another key Giuliani supporter from 2008, Rep. Frank Guinta, agrees that Giuliani could be a force, although he's not willing to support Giuliani again at this point.

"If Rudy got in the race, and if he ran a different kind of New Hampshire-based campaign, he would be a worthy opponent," Guinta said. "I think his experience and his stature warrants seriousness and brings credibility to the potential group of people running."