House Republicans ran into divisions Wednesday over the new Congress' first abortion bill, and leaders were searching for a way to advance the legislation without an embarrassing split over the issue.

Legislation scheduled for a vote Thursday would criminalize virtually all abortions for pregnancies of 20 weeks or longer. It would offer some exceptions, including for victims of rape that have already been reported to authorities.

Some Republicans, including female members of Congress, objected to that requirement, saying that many women feel too distressed to report rapes and should not be penalized. A 2013 Justice Department report calculated that just 35 percent of rapes and sexual assaults were reported to police.

"The issue becomes, we're questioning the woman's word," said Rep. Renee Ellmers, R-N.C. "We have to be compassionate to women when they're in a crisis situation."

There were also objections to the bill's exemption for minors who are victims of incest and have reported the incident.

"So the exception would apply to a 16-year-old but not a 19-year-old?" said Rep. Charles Dent, R-Pa. "I mean, incest is incest."

The divisiveness over the measure comes as Republicans, looking ahead to the 2016 presidential and congressional elections, hope to increase their support from women. In control of the entire Congress for the first time in eight years, Republicans also want to demonstrate that they can focus on issues that matter to voters and not get bogged down in gridlock.

"My own view on this stuff is I prefer we as a Republican conference avoid these very contentious social issues," Dent said.

Thursday's debate was timed to coincide with the annual march on Washington by abortion foes marking the anniversary of the Supreme Court's Roe v. Wade decision in 1973 legalizing abortion.

Rep. Trent Franks, R-Ariz., a chief sponsor of the bill, called it "a sincere effort" to protect women and "their unborn, pain-capable child from the atrocity of late-term abortion." He also said GOP leaders "want to try to create as much unity as we can."

The White House has threatened to veto the legislation, calling it "an assault on a woman's right to choose."

Democrats were strongly against the legislation and said the measure was nothing more than a political gesture.

"This is not only insulting to the women of this country, but it's just another pointless exercise in political posturing," said Rep. Carolyn Maloney, D-N.Y. "It will never become law."

The GOP rift on the issue was discussed Wednesday at a private meeting of House Republicans, who by a large majority are strongly anti-abortion.

House Majority Leader Kevin McCarthy, R-Calif., said in a brief interview that he believed the House would debate the bill as planned. But he did not rule out changes.

"We're moving forward," he said. "There's a discussion and we're continuing to have discussions."

The legislation would also allow an exception where an abortion is necessary to save the mother's life.

Under the bill, those performing the outlawed abortions could face fines or imprisonment of up to five years.

A report this week by the nonpartisan Congressional Budget Office cited estimates by the federal Centers for Disease Control and Prevention that about 10,000 abortions in the U.S. are performed annually 20 weeks or later into pregnancies. The budget office estimated that if the bill became law, three-fourths of those abortions would end up occurring before the 20th week.

The House approved a similar version of the bill in 2013, but the measure was never considered in the Senate, which was then controlled by Democrats. Its fate remains uncertain in the Senate, where anti-abortion sentiment is less strong than in the House.