CONCORD, N.H. (AP) -- Republican presidential candidate Herman Cain clarified his position on abortion Thursday, a day after saying he opposed the procedure but didn't believe the government or other people should have a role in the decision to terminate a pregnancy.

Cain issued the statement after rival Republican candidate Rick Santorum accused the Georgia businessman of holding a view common to supporters of abortion rights and said Cain was not a true conservative. It was the third time in less than a week that Cain had made a statement only to take it back after facing criticism.

In an interview Wednesday with CNN, Cain said he believes life begins at conception. "And abortion under no circumstances," he added. But Cain also said "it's not the government's role or anybody else's role to make that decision."

Asked whether his personal views would become a "directive to the nation," should he become president, Cain said they wouldn't.

"I can have an opinion on an issue without it being a directive on the nation," he said. "The government shouldn't be trying to tell people everything to do, especially when it comes to social decisions that they need to make."

Campaigning in New Hampshire on Thursday, Santorum accused Cain of misleading voters about his conservative credentials.

"It's basically the position that just about every pro-choice politician has in America," Santorum told The Associated Press. "I don't know too many pro-choice politicians who are for abortion, who want more abortions ... but they say the decision is a choice the government shouldn't be involved in."

Santorum added: "That is Herman Cain's position, which does not make him pro-life. That is the quintessential pro-choice position on abortion."

In a statement released in the wake of Santorum's remarks, Cain said he thought he was being asked on CNN whether he would, as president, "order" people to not seek abortions.

"My answer was focused on the role of the president. The president has no constitutional authority to order any such action by anyone. That was the point I was trying to convey," he said. "As to my political policy view on abortion, I am 100 percent pro-life. End of story."

Cain said he would do "everything that a president can do, consistent with his constitutional role, to advance the culture of life."

Cain has walked back two other statements recently. A day after saying that he wanted a potentially deadly electrified fence to keep out illegal immigrants, he told NBC on Sunday that he had been joking. On Tuesday, hours before a GOP candidate debate, Cain told CNN that as president he would negotiate for the release of American hostages held by al-Qaida in exchange for all prisoners at the Guantanamo Bay facility in Cuba. He later said he had misunderstood the question and that he would not negotiate with the terrorist group.

Santorum, a former U.S. senator from Pennsylvania, has been campaigning aggressively in early voting Iowa, where he gets high marks from conservative activists but registers little support in public polls. Cain, meanwhile, has been rising in the polls, both in New Hampshire and nationally.

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