Mitt Romney debuted a new TV ad this week that softens his positions on abortion and contraception and urges women voters to focus more on economic issues than social ones.

At a moment when women are seen as increasingly crucial to the outcome of the election, Romney is trying to build on gains he has made in recent polls. He also is trying to reverse the advantage that President Obama has built this year in part by hammering at Romney’s many statements on women’s health issues during the Republican primary season, when the GOP candidate described himself as “severely conservative.”

Obama’s campaign quickly seized on the latest ad as another example of Romney’s effort to erase the conservative stands he took during the GOP primaries. Obama’s strongest moments in Tuesday’s debate came when he accused Romney of not being honest about his own positions. The president hopes to use Romney’s new ad in the same way; Obama talked about women’s health issues at a rally in Iowa on Wednesday afternoon and is expected to do the same at an event in Ohio.

At the rally here, Obama told a boisterous crowd of about 2,000: “Governor Romney didn’t want to talk last night about how he wants to end funding for Planned Parenthood. He didn’t want to talk about it because he can’t sell it. I don’t think your boss should control the health care you get. I don’t think insurers should control the health care you get. I certainly don’t think politicians should control the health care you get.”

Romney’s new ad, called “Sarah,” features a young woman speaking into the camera, saying that Obama ads accusing Romney of wanting to ban all abortions and contraception “concerned” her. “So I looked into it,” the woman says. “Turns out, Romney doesn’t oppose contraception at all. In fact, he thinks abortion should be an option in cases of rape, incest or to save a mother’s life.”

Finally, the woman pivots away from social issues — something that Romney would like all voters to do — with this last comment: “This issue is important to me,” she says. “But I’m more concerned about the debt our children could be left with.”

Several Romney spokespeople declined to say anything on the record about the ad. It’s not clear where it’s playing, but copies are available on YouTube, captured from TV screens in the Washington area, where campaigns often make small ad buys to capture the attention of political journalists or to reach vote-rich Northern Virginia.

The Obama campaign, however, was eager to talk about “Sarah.” Obama spokeswoman Lis Smith issued a lengthy statement noting Romney’s positions on abortion and contraception, including his support for the so-called ”Blunt Amendment,” a failed measure that would have allowed employers to opt out of a mandate to cover contraceptives in employee health plans.

Smith also noted Romney’s statement during a Republican primary debate in December 2007 that he would “welcome” a law calling for no abortions “at all, period.” Romney also has called Roe v. Wade a “bad law.”

“Women are on to Mitt Romney,” Smith said. “That’s why he’s trying so hard to spin away the truth about his extreme positions, like during last night’s debate when he dishonestly claimed that he doesn’t ‘believe employers should tell someone whether they could have contraceptive care or not.’ These are the facts: He’d put women’s health-care decisions in the hands of their employers, has said he’d be ‘delighted’ to sign a bill banning all abortions, and called Roe v. Wade ‘one of the darkest moments in Supreme Court history,’ while pledging to appoint Supreme Court justices who will overturn it. Women simply can’t trust him to stand up for them.”

While the new “Sarah” ad doesn’t say Romney supports abortion, noting merely that he would allow for exceptions in the case of rape, incest of when the life of the mother is at stake, it’s clear the ad’s purpose is to soften public perceptions of his positions on such issues.

That effort to reach out to women has proven tricky for Romney, who is trying to appeal to moderate general-election voters without alienating the conservatives he courted during the primaries — and whom he needs to remain enthusiastic through Election Day. Last week Romney told the Des Moines Register: “There’s no legislation with regards to abortion that I’m familiar with that would become part of my agenda.” But the next day, conservative leaders came to Romney’s defense, as if to assuage supporters who might have been alarmed by what the candidate said.

Similarly, one explanation for why “Sarah” might be running only in isolated locations is the fact that in Northern Virginia, for instance, it reaches moderate women voters but falls short of the conservative households elsewhere in the state who might be turned off.

Obama and his advisers will continue to go after Romney for his statements on women’s health issues. Both campaign manager Jim Messina and senior White House adviser David Plouffe said after Tuesday’s debate at Hofstra University that woman make up a majority of undecided voters in the swing states.

Romney’s comments on contraception during the debate, Plouffe said, were “a bald-faced dishonesty.” Despite his prior support of the Blunt Amendment, Romney said: “I don’t believe employers should tell someone whether they could have contraceptive care or not. Every woman in America should have access to contraceptives. And the president’s statement of my policy is completely and totally wrong.”

“The women’s health-care exchange was really important,” Plouffe told reporters. “I think it’s going to take on increased importance because there’s going to be scrutiny on it.