Protesters stand with signs in front of Southwestern Women’s Surgery Center in Dallas on Oct. 28, 2013. (Larry W. Smith/European Pressphoto Agency)

Reproductive rights groups on Monday filed a lawsuit against the state of Texas over regulations set to go into effect next week requiring some aborted and miscarried fetuses to be cremated or buried.

The rule, finalized last month, forbids hospitals, abortion clinics and other health centers from treating tissue leftover from abortion and miscarriage procedures as medical waste, regardless of the wishes of the woman. Supporters say it recognizes the dignity of the unborn child and will prevent the tissue from being used for medical research. Critics, however, called it an unnecessary regulation designed to shame women and burden abortion clinics with costly regulations.

The Center for Reproductive Rights and several abortion providers said Monday that they filed suit in federal court on the grounds that the regulations are medically unnecessary and therefore conflict with a Supreme Court ruling earlier this year. They are asking for the rule to be blocked. Louisiana and Indiana passed similar laws but both have been mired in legal challenges.

“These regulations are an insult to Texas women, the rule of law and the U.S. Supreme Court, which declared less than six months ago that medically unnecessary restrictions on abortion access are unconstitutional,” Nancy Northup, president of the Center for Reproductive Rights, said in a statement. “These insidious regulations are a new low in Texas’ long history of denying women the respect that they deserve to make their own decision about their lives and their healthcare.”

The rule has the support of Gov. Greg Abbott (R), who through a spokeswoman Monday said that he would like to see it codified by an act of the state legislature next year.

“Governor Abbott believes human and fetal remains should not be treated like medical waste, and the proposed rule changes affirms the value and dignity of all life,” spokeswoman Ciara Matthews said in an email. “For the unborn, the mothers and the hospital and clinic staff, the governor believes it is imperative to establish higher standards that reflect our respect for the sanctity of life.”

It was also lauded by Texas Right to Life, a group that opposes abortion rights. But it added that passing a law next year should be a lower priority than other abortion-related bills, such as one that would outlaw a common second-trimester procedure called dilation and extraction. Opponents refer to it as “dismemberment.”

“With limited time and political will, Pro-Life efforts must not be focused on how babies are discarded after they are aborted,” the group said in a statement on its website. “Rather, the Pro-Life movement should prioritize bills that affirm preborn children’s constitutional Right to Life and will immediately save lives, like the Dismemberment Abortion Ban.”