CNN

Washington (CNN) - The problematic intersection of health care and abortion politics was highlighted again Monday as religious abortion rights supporters demanded changes to reform legislation recently passed by the House of Representatives.

Members of the Religious Coalition for Reproductive Choice held a news conference calling on the Senate to alter language in the House bill that places explicit restrictions on federal funding for abortion.

"We call on the Senate to ensure that the health care reform is freed of religious doctrine and restrictions that would prevent women from making their own reproductive health care choices," said the Rev. Carlton Veazey, the head of the coalition.

"We are ... very disappointed, but we are not defeated," declared Jon O'Brien, head of the group Catholics for Choice, which is part of the coalition. "We believe that health care reform is not about covering some parts of some people, but all parts of everybody."

The coalition is an umbrella organization composed of representatives of a variety of progressive Catholic, Protestant, Jewish and other groups.

Religious leaders have been split over the issue of abortion coverage. The U.S. Conference of Catholic Bishops pushed successfully to amend the House bill to prohibit abortion coverage in a government-run health insurance plan, as well as in private plans that accept anyone using government subsidies to buy insurance coverage.

Current law restricts federal funding for abortions to cases of rape, incest or to save the life of the mother.

Under the House bill, people would be permitted to buy supplemental coverage for abortions with their own money. Abortion rights groups have called the idea discriminatory and preposterous, arguing that women rarely plan ahead for an abortion.