The Republican-led House approved the bill by a largely party-line vote of 242-184. An earlier version was pulled by House Republican leaders in January after a revolt by some Republican women in the chamber.
House Judiciary Committee Chairman Bob Goodlatte called Wednesday's vote "a victory for the most innocent and defenseless among us, our children."
"Extensive medical research shows that unborn children begin to feel pain by 20 weeks post fertilization, and probably earlier," the Virginia Republican said.
The bill, called the Pain-Capable Unborn Child Protection Act, faces an uncertain fate in the Senate. White House spokesman Josh Earnest said on Wednesday the Obama administration continued to strongly oppose the bill.
"It's disgraceful that House Republicans would be considering a party-line vote on a piece of legislation that would continue to impose even additional harsh burdens on survivors of sexual assault, rape and incest," Earnest told a White House briefing before Wednesday's vote.
The Center for Reproductive Rights called the bill "cruel and unconstitutional," saying it contained exceptions only for women with life-threatening conditions, rape survivors who have gotten medical care or counseling at least 48 hours before seeking an abortion, and minors who reported rape or incest to law enforcement or child protection agencies.