SAN FRANCISCO — California’s legal battle over same-sex nuptials is now headed to the U.S. Supreme Court, the final chapter in four years of litigation over the constitutionality of Proposition 8’s ban on gay marriage.

In a brief order Tuesday, the 9th U.S. Circuit Court of Appeals said a majority of the court’s active judges voted against reconsidering a three-judge panel’s decision to overturn the voter-approved 2008 state constitutional amendment. Three dissenting 9th Circuit judges who favored review called the panel’s ruling a “gross misapplication” of the law that “roundly trumped California’s democratic process.” The two judges who voted to overturn the ban last February reiterated Tuesday that their decision was limited to the situation in California.

Lawyers in the case expect the U.S. Supreme Court to review Proposition 8 this fall and decide its constitutionality next June. Until the Supreme Court acts, the 9th Circuit’s order will be on hold and Proposition 8 will remain in effect.

“The end is now in sight,” said Chad Griffin, who started a group that is financing the legal battle against Proposition 8.

The dissents in Tuesday’s 9th Circuit decision showed that courts remain divided. Judge Diarmuid O’Scannlain, joined by two other jurists, wrote that even President Obama favored letting states decide “in a respectful way” whether to permit gays to marry.

“Today our court has silenced any such respectful conversation,” wrote O’Scannlain.