The underlying issue in the case, to be heard in the fall, is a blocked Kentucky law that abortion rights supporters say would have effectively banned a standard abortion method in the second trimester of pregnancy.
AdFive days later, the Supreme Court ruled 5-4 to strike down an unrelated Louisiana law regulating abortion clinics.
But Cameron, who became attorney general in 2019, said the reasoning used by the high court called into question the ruling against the Kentucky law.
The appeals court, however, rejected his efforts to intervene, prompting his appeal to the Supreme Court.
In February, Kentucky's Republican-led legislature gave Cameron the power to seek civil and criminal penalties for any violation of Kentuckyās abortion laws.