Women’s rights and medical groups have called on Gov. Bill Haslam of Tennessee to veto legislation that would allow criminal assault charges to be filed against women who use illegal drugs during pregnancy. Critics say the measure will harm babies because pregnant women will be afraid to seek medical care.

At a time of rising concern about narcotics addiction, the bill was passed last week by bipartisan majorities in both houses of the Tennessee legislature. It received crucial support from the district attorney in Memphis, Amy Weirich, who said the threat of jail was needed as a “velvet hammer” to force mothers into court-supervised drug treatment.

“We have too many women in Tennessee giving multiple births to drug-dependent babies,” Ms. Weirich said. “The focus of the legislation is not to punish these mothers. It’s to get them help for their drug addiction, using the drug courts.”

While states have used criminal laws and child-welfare rules to punish mothers who use drugs, the Tennessee bill would be the first of its kind to detail criminal charges when a fetus or newborn is deemed to be harmed by illegal narcotics.