The 227-188 vote Tuesday was mainly along party lines, with six Democrats voting yes, one Republican voting no and another voting present, the New York Times reported.
"Here we go again," Rep. Barbara Lee, D-Calif. "It's another battle in the war on women."
Republicans, dogged by accusations that they are hostile to women, said Democrats unfairly characterized their intentions.
"I will say it again," Rep. Virginia Foxx, R-N.C., said, "we are not attacking women's healthcare."
Existing law such as the Hyde Amendment restricts federal financing for abortion services. Since the Hyde Amendment must be renewed annually, Republicans said their proposal merely would codify what has been the law of the land.
Some Republicans said they would prefer discussing jobs and the economy rather than an abortion bill, which will go nowhere in the Democratic-majority Senate, the Times said.
"I've always said that we ought to avoid taking on these hot-button social issues; they don't do us any good," Rep. Charlie Dent, R-Pa., said.
While he voted for the bill, Dent also noted how some of his colleagues were so ill-prepared to discuss women's health issues that the leadership has had to counsel its members on how to approach the topic with greater sensitivity.
"Here's my suggestion for a communications strategy for some of these guys," Dent said. "Four words: Shut the bleep up."
Some Democrats, too, said they think their party would be better served discussing jobs and the economy, the Times said.
"I'm a skeptic," said Rep. Peter Welch, D-Vt. "The people we represent need jobs, need better incomes and want us to focus on the economy. To the extent that we get involved in issues that take us away from that, it legitimately undercuts our credibility."