(Reuters) - Four married lesbian couples expecting children have filed a lawsuit in Tennessee seeking to overturn a new state law that critics say could deny rights to same-sex couples by requiring strict adherence to terms such as “husband.”

Governor Bill Haslam on Friday signed a law that requires that words in state statutes be interpreted with “natural and ordinary meaning.” That would include words like “husband” and “wife,” which the same-sex plaintiffs say will interfere with their parental rights.

“Regardless of the actions of the Tennessee General Assembly, the right to be recognized as the parent of a child of one’s marriage is a right which deserves Constitutional protection,” the lawsuit said.

One of the law’s legislative sponsors has argued it had nothing to do with same-sex marriage, but the Knoxville News Sentinel has reported that another sponsor said he proposed the measure partly to compel courts to side more closely with the dissenting opinion in the U.S. Supreme Court’s landmark 2015 ruling in the case of Obergefell v. Hodges which legalized same-sex marriage.

Haslam said after signing the bill that he believes the law will not change how courts interpret legal precedent. The governor’s office declined comment on Tuesday, citing pending litigation.

But Julia Tate-Keith, who filed the lawsuit on behalf of the couples, said the law’s aim was to take away same-sex rights.

“It absolutely is about denying gay people equal protection under the law,” she said on Tuesday.

Plaintiffs Charitey and Heather Mackenzie, Crystal Dawn and Terra Mears, Elizabeth and Heather Broadaway, and Kathrine and Emilie Guthrie filed the suit on Monday in Davidson County Chancery Court in Nashville. Each couple has one pregnant partner due to give birth this year.

The suit cites a portion of Tennessee law says that a “child born to a married woman as a result of artificial insemination, with consent of the married woman’s husband, is deemed to be the legitimate child of the husband and wife.”

Tate-Keith said that while Tennessee interpreted “husband” to include the female spouses of lesbians after the high-court ruling, that could change under the new “natural meaning” law.

As a result, she said, under certain scenarios children could be denied health insurance coverage, hospital visitation, social security benefits or custody rights.

Tennessee Attorney General Herbert Slatery, a Republican, said in an April opinion that the law could in some cases conflict with Supreme Court’s same-sex ruling.

No hearings have been scheduled, Tate-Keith said.