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Same-sex couples in Louisiana could wait nearly a month for marriage licenses after officials in the state advised clerks of court about a provision of the Supreme Court’s rules that would conceivably allow the justices to rehear the matter.

Officials in East Baton Rouge Parish, citing the advice of their counsel and the Louisiana Clerks of Court Association, said in a statement on Friday that they would “not be issuing same-sex marriage licenses until the period for Supreme Court rehearing has elapsed and all other legal necessities are in place.”

Under the court’s rules, a request for a rehearing must be filed “within 25 days after entry of the judgment or decision,” but a justice can extend or shorten that time frame. Experts said that a rehearing is unlikely, in part because the court’s rules require that a majority of the justices agree to such a proposal.

The Clerks of Court Association did not immediately respond to a message, and officials in other parishes said they planned to follow the group’s advice.

“In Louisiana, we’re trying to do this correctly where we won’t have an issue where something will come down at a later time and cause licenses to be rescinded,” said H. Lynn Jones II, the clerk of court in Calcasieu Parish.

Mr. Jones, whose parish has about 197,000 residents, said same-sex couples had reached out to his office on Friday, but were told that the Calcasieu authorities would not immediately issue licenses.

Separately, the Louisiana Department of Health and Hospitals said the state’s same-sex marriage ban remained in force, and Attorney General James D. Caldwell’s office said it had “found nothing in today’s decision that makes the court’s order effective immediately.”