Rather than sign, Romney published a pledge on the website of the conservative magazine National Review on Saturday, including an explanation why he couldn’t sign the Susan B. Anthony pact. His reasons were twofold: By his reading, the pledge required cutting off federal funds to hospitals. In addition, Romney said that, if elected, he did not want to be hobbled by the pledge’s requirement that nominees for the Cabinet and other key positions oppose abortion.

“I think there’s only one way of looking at it, and that is not signing it revealed a weakness in conviction,’’ she said. “I don’t think there’s any other way of looking at it.’’

Romney’s decision spurred a rebuke from the organization and quickly roiled the presidential waters. Marjorie Dannenfelser, president of the Susan B. Anthony List, said she was disappointed in Romney, whom she considered an ally in the antiabortion movement.

Santorum was the first to sign, on June 8, and the others followed suit last week. But Romney declined, along with Herman Cain, the former chief executive of a pizza chain, and Gary Johnson, former governor of New Mexico.

The newly minted pledge — the first the Susan B. Anthony List has authored — has been signed by five GOP candidates: US Representatives Michele Bachmann of Minnesota and Ron Paul of Texas, Newt Gingrich, former House speaker, Tim Pawlenty, former governor of Minnesota, and Rick Santorum, former senator of Pennsylvania.

The pledge was drafted by a group called the Susan B. Anthony List, a nearly 20-year-old organization named for the turn-of-the-century suffragist who also wrote about her objections to abortion. The group backs candidates who oppose abortion, serving as a conservative counterpart to the group Emily’s List, which aids candidates who support abortion rights.

“He may have a perfectly rational expla nation, but he’s going to have to convince people of that,’’ said Carter Wrenn, a GOP political consultant in North Carolina who is not affiliated with any candidate. “If his answer satisfies people, then he’s fine. But if he doesn’t, then he could have a problem.’’

Romney insists that his antiabortion credentials are rock-solid, but that he couldn’t sign the pledge because it would cripple hospitals dependent on federal payments such as Medicare and tie his hands as president. The decision quickly drew broadsides from GOP opponents who sensed a new vulnerability in the presumed front-runner, and the possibility that socially conservative voters would have new doubts about Romney.

Last week, Romney declined to sign a new pledge that, among other things, would ban federal funds to any institution that pays for abortions or affiliates with an abortion provider.

WASHINGTON — Mitt Romney has long battled the perception that he has waffled on social policy issues crucial to Republican voters, such as abortion and gay rights. Now the former Massachusetts governor’s refusal to sign an antiabortion pledge that five other GOP contenders support has put him on the defensive again.

“As much as I share the goals of the Susan B. Anthony List, its well-meaning pledge is overly broad and would have unintended consequences. That is why I could not sign it,’’ he wrote. A spokeswoman added to his comments over the weekend, saying the pledge “calls for legislation to strip taxpayer funding from thousands of health care facilities, including VA hospitals around the country, and strictly limits the choices a president would have to appoint federal officials’’ and that he remains “firmly pro-life.’’ A spokesman yesterday declined to comment beyond the statement over the weekend.

Dannenfelser said Romney was misreading the pledge, which she said does not require a ban on funds for hospitals.

The pledge requires signers to “advance pro-life legislation to permanently end all taxpayer funding of abortion in all domestic and international spending programs, and defund Planned Parenthood and all other contractors and recipients of federal funds with affiliates that perform or fund abortions.’’

But there was no confusion, she said, about the appointments issue. Romney’s unwillingness to agree to that, she said, meant that he lacked commitment on that part of the pledge.

Romney wasn’t alone in his reluctance to sign. Cain wouldn’t sign because of concern about separation of executive and congressional powers, and Johnson, like Romney, felt that requiring antiabortion appointments would hinder him as president.

Santorum criticized Romney shortly after the former governor declined to sign.

Bachmann followed suit, calling Romney’s decision “distressing’’ and urging him to reconsider — “just as he reconsidered his position on the life issue during the last campaign.’’

Bachmann’s comment was a reference to Romney’s problems in convincing voters that he’s been politically consistent throughout his career. It is a difficult balancing act for a liberal Massachusetts former governor, who ran for office twice here supporting abortion rights, and in two presidential campaigns has had to seek support from conservative Republican activists.

In the last year, he has also had to defend himself from criticism that he supported a health insurance mandate when as governor he signed the Massachusetts health care law that served as the model for the sweeping national health overhaul. His defense is that he supported a state government solution and not a national policy. Conservative commentator Charles Krauthammer defended Romney yesterday, calling him “strongly prolife’’ and calling the criticism from his opponents a “cheap shot.’’

But Timothy M. Hagle University of Iowa political science professor, said Romney may make himself vulnerable to more criticism for inconsistency by not agreeing to the antiabortion pledge.

“You hear this flip-flopper kind of a thing where he’s just not solid on it,’’ he said. “When he doesn’t take the pledge, it opens up that question again.’’

Because Romney has put few resources in Iowa, Hagel said, his refusal to sign could be a further indication that he is courting moderate Republicans.

“It allows him to be able to speak to the folks who maybe are a little closer towards the middle on this issue. That should help him in the general election,’’ Hagel said. “Of course, the problem always is that when you stake out those middle positions during the primary season, you may not get the nomination.’’

Theo Emery can be reached at temery@globe.com. Follow him on Twitter @temery.

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