Story Highlights• GOP presidential candidate urges focus on his public service
• Ex-New York mayor also says he favors public funding of abortions
• Supreme Court has last word on abortion, Giuliani says
• Now is not right time to revisit "don't ask, don't tell," he says
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TALLAHASSEE, Florida (CNN) -- Republican presidential hopeful Rudy Giuliani said Wednesday that voters should focus on his record rather than on a "rocky" personal life that includes three marriages and an estrangement from his only son.
"I've had a very extensive record of success, failure. Nobody's ever questioned my honesty and integrity about the things that I do," Giuliani said in a wide-ranging interview with CNN correspondent Dana Bash on the campaign trail in Florida. "So, look at that. Look at my public record."
"My personal life, I've made mistakes," Giuliani said. "I've had a rocky road. I regret them. They are between me, God, my conscience and the people involved." (Watch Giuliani's life, wife become tabloid fodder )
On the hot-button issue of abortion, Giuliani said that while he believes abortion is wrong, he considers it an individual constitutional right and might support public financing for abortions in some cases if necessary to protect that right. (Watch Giuliani say he hates abortion )
However, the former New York City mayor said support for abortion rights would not be a "litmus test" for his Supreme Court appointments if he's elected president, and he would leave it up to the justices to decide if the landmark Roe v. Wade decision legalizing abortion should stand.
Giuliani also said he expects fierce competition for the GOP nomination from Arizona Sen. John McCain, who "is never going to be done."
"I don't know if I'm going to beat him or he's going to beat me in New Hampshire. But if I do beat him in New Hampshire, I expect to see him in South Carolina, and I expect to see him in California and I expect to see him every place else," he said. "This is a very, very strong man, a very determined man."
Assuaging conservatives on abortion
Giuliani's support for abortion rights has given pause to social conservatives within the GOP base, who make up an important constituency in the presidential nominating process. In a bid to assuage them, he has vowed to nominate "strict constructionist" judges to the federal bench who, he says, would interpret the constitutionality of laws, rather than legislate their own views from the bench.
Giuliani told Bash that "a strict constructionist judge can come to either conclusion about Roe against Wade. They can look at it and say, 'Wrongly decided. ... We will overturn it.' They can look at it and say, 'It has been the law for this period of time, therefore we are going to respect the precedent.'
"I would leave it up to them. I would not have a litmus test on that."
In a 1989 speech now being widely circulated on the Internet, Giuliani called for public funding of abortions for poor women, saying, "We cannot deny any woman the right to make her own decision about abortion because she lacks resources."
Asked by Bash if he would maintain that position as president, Giuliani said "probably."
"I would have to re-examine all of those issues and exactly what was at stake then -- that was a long time ago," he said. "When I was mayor, adoptions went up, abortions went down. But ultimately, it's a constitutional right, and therefore if it's a constitutional right ... you have to make sure that people are protected."
Pressed if he would support public funding for abortions, Giuliani said, "If it would deprive someone of a constitutional right, yes, if that's the status of the law, then I would, yes."
After the interview, Giuliani's campaign clarified that if elected, he would not seek to change current federal law, which limits public funding for abortions to cases of rape, incest or where the life of the pregnant woman is in danger.
Doesn't support same-sex marriage
Giuliani also said that while "I don't think there should be discrimination against gays," he does not support same-sex marriage and also believes the U.S. military should not re-examine its "don't ask, don't tell" policy governing gay and lesbian troops "in a time of war." (Watch Giuliani stake out his positions on abortion and gay rights )
"When we get out of the crisis, when we get out of the situation, we can consistently review it and look at it. But it shouldn't be done right now," he said. "It would be a very big mistake to re-raise that issue right now when we are dealing not just with Iraq but this entire war on terror."
The "don't ask, don't tell" policy bars gay men and lesbians from serving in the military if they publicly disclose their sexual identity.
Giuliani, who was treated for prostate cancer in 2000, told Bash that all of his subsequent medical screenings have been negative and that "for all intents and purposes, the cancer is cured."
"I'm very healthy now," he said. "But, of course, I get tested every six months, which you're supposed to do."
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