"She seems like a very well-qualified person and somebody that - certainly not somebody that I'd appoint, but I don't think she'd be sombody that I would, you know, fight the last mile to try to stop her," Giuliani told POLITICO at a fundraiser for New York GOP gubernatorial hopeful Rick Lazio.
"I don't think that she's that kind of extremist that you would do that," he added.
Giuliani, a GOP presidential candidate in 2008, spoke hours after Obama introduced Kagan, a New Yorker and former Harvard Law School dean, as his choice.
"I think the biggest issue she's going to have is the military one..about the ROTC," he said, referring to her wanting to ban military recruitment when she was Harvard because of the military's ban on gays serving openly. "I don't think she's going to have too many legal issues to deal with, in part because she's not been a judge" or practicing privately in cases.
"She's got something the left is worried about, and something the right is worried about - the left is worried about her support for executive power and the right is worried about her on almost every other issue," Giuliani said, chuckling.
He said while he hasn't personally studied her record, "I've always been a big believer that the president gets to select and then the Senate rejects if the person is really unqualified.
"Because we elect a president, and we expect that he's going to appoint somebody that fits his basic political philsophy, and she does not seem to me to be an extremist," he said. "If he'd picked somebody that would be an extremist, then I think that would be much more of a battle."
Asked whether Obama is drawing from the same rarified Ivy League pool for his picks, Giuliani - who was raised in Brooklyn and Long Island and went to Manhattan College and New York University law school - said it wasn't fair to blame the Democratic president for that, since the other members of the court all have similar backgrounds.
"Sure, it would be better to have a Supreme Court that had a little more diversity with regard to educational background," he said, but added , "They may all come from Harvard and Yale, but they seem like eight very different people."