Supporters of the law though say it is necessary to protect the safety of women and argue that the restrictions are not onerous.
A state judge on Wednesday granted a temporary injunction blocking North Dakota officials from enforcing the law, while he weighs its constitutionality.
The Center also filed a federal lawsuit against the two other laws signed in March, one banning abortion after about six weeks of pregnancy, and another barring genetic and gender discrimination in abortions.
The six-week abortion ban is considered one of the strictest in the nation. Its passage sparked outrage among abortion-rights supporters, who have charged that Republicans are undermining access to healthcare for women.
A federal judge on July 22 blocked the ban from taking effect, calling it “clearly” unconstitutional.