Last year, 29 percent of Mississippi’s same-sex-couple households were raising children younger than 18 — the highest percentage of any state in the nation, the complaint said.

“The Mississippi Adoption Ban writes inequality into Mississippi law by requiring that married gay and lesbian couples and parents be treated differently than all other married couples in Mississippi, unequivocally barring them from adoption without regard to their circumstances,” the complaint said. It called the ban “an outdated relic of a time when courts and legislature believed that it was somehow O.K. to discriminate against gay people simply because they are gay.”

Neither the governor’s office nor the state attorney general’s office returned messages Tuesday afternoon, asking whether the state would fight to uphold the ban.

Roberta Kaplan, the New York lawyer handling the case, said that after the Supreme Court ruling, it seemed obvious to her and her clients that “the time was right to challenge the adoption ban and get it cleaned up.”

That the case now seems more likely to be a mop-up operation than an all-out legal confrontation is an indicator of just how swiftly the social change has taken hold.

“In the federal courts, I’m pretty confident Obergefell will be construed broadly,” said Ronald Krotoszynski, a constitutional law professor at the University of Alabama, referring to the Supreme Court ruling on same-sex marriages. “I think it would be hard to draw a principled distinction between marriage and adoption, so it shouldn’t be a hard case.”