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It was a casual aside from Jeb Bush, but it could haunt him throughout a campaign in which women’s votes — and issues — may prove pivotal.

During an interview on Tuesday with religious conservatives, Mr. Bush suggested that the federal government had overfunded women’s health.

“I’m not sure we need half a billion dollars for women’s health issues,” Mr. Bush said at a Southern Baptist Convention event in Nashville.

For perspective, the federal government spends about $1 trillion a year on health care.

Amid a storm of Democratic mockery, Mr. Bush backtracked within a few hours, saying he had misspoken.

The assertion came in the middle of his answer to a question about defunding Planned Parenthood, the subject of hidden-camera videos that have portrayed its employees in unflattering ways.

Mr. Bush, a former governor of Florida, said the federal government should stop financing Planned Parenthood. He then veered off course, into a discussion of what could be done instead with the $500 million in federal funds the organization receives annually.

“You could take dollar for dollar — although I’m not sure we need half a billion dollars for women’s health issues,” he said, “but if you took, dollar for dollar, there are many extraordinary fine organizations, community health organizations, that exist, federally sponsored organizations, to provide quality care for women on a variety of health issues.”

The remark highlighted a larger problem for Mr. Bush: Out of office for eight years, he has occasionally stumbled in interviews. He spent days struggling to answer whether he would have invaded Iraq even with hindsight knowledge about intelligence failures. At first, he said he would have; then, he said he had misheard the question; later, he said he did not wish to answer the question out of sensitivity to veterans; finally, he said he would not have invaded the country.

In a statement on Tuesday night, Mr. Bush sought to clarify his original wording: “With regards to women’s health funding broadly, I misspoke, as there are countless community health centers, rural clinics, and other women’s health organizations that need to be fully funded. They provide critical services to all, but particularly low-income women who don’t have the access they need.”

Still, Mr. Bush’s original language earned a rebuke on Twitter from Hillary Rodham Clinton’s campaign: “You are absolutely, unequivocally wrong.”

At an event in Denver on Tuesday night, Mrs. Clinton expanded her critique, saying of Mr. Bush “He’s got no problem giving billions away to the wealthy and big corporations. I guess women’s health just isn’t a priority for him.”

Other Democrats, some of whom are supporting Mrs. Clinton in her quest to become the country’s first woman to be elected president, also weighed in.

Dan Pfeiffer, a former communications director for President Obama, posted a message on Twitter mocking Mr. Bush. “A few more months of this and the G.O.P. will be wishing for a candidate with the political skills of Mitt Romney,” he wrote.