The increasingly contentious fight for the White House moved from the debate stage back to the campaign trail on Wednesday as President Obama, Mitt Romney and their running mates traversed the nation’s battleground states, seeking an advantage from Tuesday’s fiery town-hall forum.

A day after Obama and Romney squared off in New York, the reverberations — and recriminations — flew as both sides tried to reframe a race that had been tilting in Romney’s favor after the first presidential debate.

But it will take days to determine the effect of Tuesday night’s event, and the candidates — as animated on Wednesday as they were onstage together — tried to re-litigate some of Tuesday’s most memorable exchanges.

Obama brought a triumphant tone to rallies in Iowa and Ohio after a performance that reassured supporters who were alarmed by his widely panned first debate two weeks earlier. Speaking to a boisterous crowd of about 2,000 in a sweaty gymnasium at an Iowa college, he mocked Romney for wanting to repeal the Affordable Care Act, the nation’s new health-care law, which includes a provision that prevents insurers from denying coverage because of preexisting conditions.

“Being a woman is not a preexisting condition,” he said, echoing a Democratic theme that Romney is insensitive to the concerns of women, a crucial voting bloc with which the Republican has recently made gains.

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Vice President Biden took the argument further at a rally in Colorado, ridiculing Romney as “sketchy,’’ especially for the debate-night comment that he had sought and received “binders full” of female job candidates while he was Massachusetts governor.

“When Governor Romney was asked a direct question about equal pay, he started talking about binders,” Biden told a crowd of 1,100 in the closely contested swing state. “Whoa! The idea that he had to go and ask where a qualified woman was, he just should have come to my house. He didn’t need a binder.”

Romney struck back, charging that Obama has “failed” women. From the economy to energy to immigration, the Republican repeated many of the same sharp critiques of Obama’s record that he delivered Tuesday night in New York.

On issue after issue, Romney brought up questions from voters in the session at Hofstra University and criticized Obama’s answers. “When it comes to his policies and his answers and his agenda, he’s pretty much running on fumes, and the American people want some real answers and a real agenda,” Romney told 3,500 people at a rally in Chesapeake, Va.

Although he didn’t claim victory, Romney said: “I have to be honest with you, I love these debates. You know, these things are great.”

Both campaigns found something to like in Tuesday’s session, the second of three encounters in what has been a closely fought presidential race focusing on a handful of key states. And even as the sprint to the Nov. 6 election resumed, they looked ahead to what is shaping up as a critical final debate on Monday in Boca Raton, Fla. The main subject will be foreign policy.

Post-debate polls declared Obama a narrow winner Tuesday night, and his aides and surrogates worked furiously on Wednesday to turn that into momentum. They focused on issues such as women’s health and Romney’s difficulties when he tried to attack the president over the White House’s handling of the Sept. 11 attack on a U.S. diplomatic post in Benghazi, Libya.

Romney has seized on the assault, which killed Ambassador J. Christopher Stevens and three other Americans, to back his contention that Obama has presided over a weakening of U.S. influence abroad. But he mistakenly said the president took weeks to call the Benghazi attack “an act of terror,” even though, as moderator Candy Crowley of CNN pointed out, the president used those words in a statement in the Rose Garden a day after the attack. Republicans criticized Crowley’s intervention.

Several Romney advisers acknowledged privately Wednesday that Obama got the better of that exchange. But publicly they said that the Libya upheaval lingers as a growing vulnerability for Obama in the campaign’s closing weeks and predicted that Libya will be a major focus of Monday’s final debate.

“I think people see it, and it’s very troubling,” Stuart Stevens, Romney’s chief strategist, said in an interview Wednesday. Repeating a charge Romney made in the debate, Stevens said, “I think the idea of leaving the White House to go to a fundraiser in Las Vegas followed by another fundraiser in Colorado is something that doesn’t sit well with people, when you now have a sense that it was an attack and Americans died.”

Romney’s advisers said they will continue to push the campaign’s central argument that the candidate, a former chief executive, is better equipped than Obama to improve the sluggish economy. Although they generally portrayed the debate as a draw, they were encouraged by polls showing Romney bested Obama on economic issues. A CNN survey, for example, found that Obama won the debate 46 percent to 39 percent among voters who watched but that Romney came out ahead, by 18 percentage points, on the economy.

The Romney campaign on Wednesday called in star power to help, both from political circles and Hollywood: Dennis Miller introduced Romney at his Virginia rally, while former secretary of state Condoleezza Rice appeared with Romney’s running mate, Rep. Paul Ryan (Wis.) at an event outside Cleveland.

“Didn’t Mitt Romney do a great job for us last night?” Ryan asked the crowd, drawing loud cheers, before pivoting back to the key issue of female voters.

“You know, we had a discussion about how women are faring in this economy last night,” Ryan said. “A half-million women more are unemployed today than when President Obama was sworn in. . . . We need to get people back to work.”

Amy Gardner, Philip Rucker, Krissah Thompson, Felicia Sonmez, Scott Wilson and Anne Gearan contributed to this report.