WASHINGTON — President Obama charged that Mitt Romney’s policies are economically threatening to women, as the candidates in their second presidential debate on Tuesday night clashed repeatedly over who would best serve the interests of the country’s largest and most critical constituency.

With some polls offering sporadic evidence that Mr. Romney is gaining support among women in the final weeks of the campaign, the president seized every opportunity during their face-off at Hofstra University on Long Island to assert that Mr. Romney, the Republican candidate, would eliminate financing for women’s health services, block access to contraceptives, oppose equal pay and undermine the economic recovery for families in which women are the breadwinners.

“This is not just a women’s issue,” Mr. Obama said during an exchange about equal pay for women in the workplace. “This is a family issue. This is a middle-class issue. And that’s why we’ve got to fight for it.”

Mr. Romney sought to defend his policies as better for women, denying Mr. Obama’s accusations about contraception and insisting that his record as Massachusetts governor is one of inclusion and equality. Even as the debate concluded, Mr. Romney’s campaign released a television ad stressing that he does not oppose contraception and believes abortion should be legal in some cases.