Updated

On the heels of passing sweeping gun control legislation, New York Gov. Andrew Cuomo is pushing the envelope once again -- this time with a call for an abortion bill that opponents say would effectively allow late-term abortion "on demand."

Pro-life organizations and religious groups are beginning to rally against the proposal, after Cuomo declared in his Jan. 9 State of the State address that he wanted to enact a so-called "Reproductive Health Act" as part of a 10-point plan to advance "women's equality."

The governor did not dive into specifics in his address, but he is expected to push for provisions similar to those in a bill introduced by Democratic state Sen. Andrea Stewart-Cousins.

That bill contains language that would allow abortion after 24 weeks of pregnancy if it is "necessary to protect a woman's health" -- that exception is different from one protecting a woman's life and one critics say can be broadly interpreted.

Stewart-Cousins on Tuesday urged her colleagues to bring the "crucial legislation" to the floor "as soon as possible."

She said in a statement it would "ensure that regardless of what takes place on the national level, a woman's right to choose will always be protected in New York State."

But the New York State Catholic Conference earlier this month described the plan as "radical." Cardinal Timothy Dolan, archbishop of New York, wrote in a letter to Cuomo that given New York state's high abortion rate, "I am hard pressed to think of a piece of legislation that is less needed or more harmful than this one."

The conference issued a breakdown of the bill that declared it would "permit unlimited late-term abortion on demand."

The group said the "health" exception has been "broadly interpreted by the courts to include age, economic, social and emotional factors."

"It is an exception that will allow more third-trimester abortions in New York state," the group said.

Further, the conference took issue with language that would allow a "licensed health care practitioner" to perform abortions, complaining it would allow non-doctors to do the procedure. And the bill includes language to establish a "fundamental right" of women to determine the course of pregnancy, "which includes the right to carry a pregnancy to term or to terminate a pregnancy" -- the conference claims this would "preclude" certain regulation in the future.

Pro-life Democrats have likewise raised concern. Democrats for Life of America called it "the most sweeping abortion legislation in the nation" and "out of touch with the views of most Americans."

But New York Senate Democratic officials argue that the bill merely treats abortion as a "public health" issue rather than a criminal matter. As for the claim that it lets "non-doctors" perform abortions, they note that the bill still requires practitioners to have the proper training to perform the procedure or else face criminal punishment under state law.

The debate comes as pro-life advocates prepare to head to Washington this Friday for the annual March for Life. Tuesday also marked the 40th anniversary of the Supreme Court's historic Roe v. Wade decision -- an anniversary pro-life groups have used as a rallying point to press for stronger abortion restrictions.

Abortion rights supporters likewise marked the occasion.

The White House released a statement Tuesday saying: "On the 40th anniversary of Roe v. Wade, we reaffirm its historic commitment to protect the health and reproductive freedom of women across this country and stand by its guiding principle: that government should not intrude on our most private family matters, and women should be able to make their own choices about their bodies and their health care."

Cuomo had included the abortion bill as part of a broader 10-point plan he described as a "Women's Equality Act."

In his speech, he called for new laws addressing equal pay, human trafficking and domestic violence, among other issues. On abortion, he said: "Protect a woman's freedom of choice. Enact a Reproductive Health Act, because it is her body, it is her choice."

Kathleen Gallagher, director of pro-life activities for the New York State Catholic Conference, told FoxNews.com that while abortion remains controversial in the state, Cuomo could try to improve the odds of the bill passing by bundling it with the other nine provisions.