The NAACP's Maricopa County branch and the National Asian Pacific American Women's Forum on Wednesday asked the 9th U.S. Circuit Court of Appeals to reinstate the lawsuit. U.S. District Judge David G. Campbell ruled in October that they didn't have legal standing to sue.
The Arizona law makes it a felony to knowingly provide a sex- or race-based abortion.
The groups contend that the law unconstitutionally singles out Asian and black women based on stereotypes and the sponsors' beliefs that they may choose an abortion because of race or the baby's sex.
Supporters of the 2011 law say it was intended to prevent discrimination.