WASHINGTON — House Republicans have modified a tough anti-abortion bill to include exceptions for rape and incest after the GOP sponsor of the legislation raised a firestorm by declaring that very few rapes result in pregnancies.

The legislation, which challenges the 1973 Roe v. Wade Supreme Court decision on a woman’s right to abortion, would ban almost all abortions after a fetus reaches the age of 20 weeks. It is scheduled to come up for a vote in the full House next week.

On Wednesday, when the House Judiciary Committee considered the legislation, sponsor Trent Franks, R-Ariz., said that cases of “rape resulting in pregnancy are very low.” He was speaking on a proposed Democratic amendment, defeated by Republicans, that would have made exceptions to the ban in cases involving rape and incest.

Franks later revised his remark, saying he meant to say that later-term abortions rarely are the result of rapes, but Democrats pounced on his statement, saying it was another example of Republicans showing their insensitivity toward women.

They compared it with the case of former Rep. Todd Akin, R-Mo., whose run for a Senate seat last year collapsed after he said the female body is capable of blocking pregnancies in the case of “legitimate rape.”

The bill as approved by the Judiciary Committee on a party-line vote provides an exception to the ban only when an abortion is necessary to save a woman whose life is endangered by physical illnesses or injury.

But the legislation as posted Friday by the Rules Committee, which determines the procedures for next week’s floor debate, included a new exception if “the pregnancy is the result of rape, or the result of incest against a minor,” and the rape or incest has been reported to appropriate authorities prior to the abortion.

House Majority Leader Eric Cantor, R-Va., asked about possible changes to the bill Friday during a floor discussion with Democratic Whip Steny Hoyer of Maryland, responded that “there’s been a lot of discussion that I have been receiving, comments, input from members, and we’re looking at weighing those suggestions and inputs.”

Republicans determined to reverse their poor performance among women in recent elections have been quick to counter criticisms that they stand for anti-women policies.

The “Pain-Capable Unborn Child Protection Act” is similar to laws in several states that have been ruled unconstitutional or face court challenges, but the vote in the House next week will give social conservatives a rare chance to express their views on one of their most important issues. The Democratic-led Senate will probably never take up the bill.