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COLUMBIA, S.C. (CBS/AP) ― Republican presidential candidate Rudy Giuliani on Thursday defended his record favoring the use of public money for abortions, saying he wouldn't try to undo a Supreme Court ruling allowing the procedures.

"Ultimately I believe it's an individual right and a woman should make that choice," the former New York mayor said during a Statehouse news conference at which he picked up three endorsements.

Support for abortion rights is unpopular with conservatives who dominate the GOP in South Carolina, an early voting state.

Giuliani said he tells people what he thinks.

"I tell them (to) evaluate me as I am and do not expect them to agree with me on everything. I don't agree with me on everything," Giuliani said. "If that's the most important thing, then I'm comfortable with the fact you won't vote for me."

The comments came as South Carolina lawmakers push a measure that would require women seeking abortions to first view ultrasound images of their fetuses. If the South Carolina measure is approved, the state would be the first to make such a requirement. Other states require the images be made available to women.

Giuliani said states should make the call on such issues.

"The Legislature of South Carolina should make its decision about that," he said.

He also said states should make the decision whether to use public money for abortions.

However, Giuliani's campaign aides say that if elected he won't seek to change current federal law, which only allows public funding for abortions in the cases of rape and incest or when the mother's life is in jeopardy.

Conservatives and political experts in South Carolina said Giuliani's moderate stance on abortion will hamper his ability to win votes in the state.

"He's toast," said Clemson University political scientist Dave Woodard. "I think it's going to be really hard for him to overcome this in South Carolina."

While Republicans in South Carolina oppose abortion by degrees -- allowing abortions in certain circumstances, such as a mother's health, rape or incest -- there's little room on public financing, said Oran Smith, executive director of the Palmetto Family Council, an anti-abortion group.

"That's usually one of the first things off the list when you talk about things related to abortion," Smith said.

Some Giuliani supporters said the abortion issue doesn't bother them.

"I'm really for the whole package. I feel like I'm comfortable being for him," said Rosemary Byerly, a staunch abortion opponent from Inman.

But Alexia Newman, a state Republican Party first vice chairwoman who runs Spartanburg's Carolina Pregnancy Center, said she felt duped by Giuliani's recent comments to the state Republican executive committee that if elected he would appoint judges who favor a strict interpretation of the Constitution to the Supreme Court.

However, Giuliani said those comments weren't a nod in the direction of undoing Roe v. Wade.

"If I'm going to appoint strict constructionist judges, which I'm going to do, for the reason that they are going to strictly interpret the Constitution, then, as president, I have to be a strict constructionist," Giuliani said. "The present state of the law on these issues is not something that I would seek to change."

Giuliani also said the state should be left to make its own decision about the Confederate flag, which flies outside the Statehouse.

During a stop in Charleston, Giuliani was mobbed by tourists and supporters as he walked through the city's open air market, where vendors sell sea shells and sweetgrass baskets.

Giuliani scrawled his autograph on everything from tourist maps to business cards.

Giuliani went to Myrtle Beach, where he threw out the first pitch at a Pelicans minor league baseball game and then sat behind home plate to watch the game with state Treasurer Thomas Ravenel.

(© 2007 CBS Broadcasting Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)