NEW YORK — The union for longshoremen along the East Coast and Gulf of Mexico has agreed to extend its contract for 30 days, averting a possible strike that could have crippled operations at ports, including the one in Savannah, that handle about 40 percent of all U.S. container cargo, a federal mediator announced Friday.

The extension came after the union and an alliance of port operators and shipping lines resolved one of the stickier points in their months-long contract negotiations, involving royalty payments to the longshoremen for each container they unload.

Negotiations will continue until at least midnight Jan. 28. Some important contract issues remain to be resolved, but the head of the Federal Mediation and Conciliation Service, George Cohen, said the agreement on royalties was “a major positive step forward.”

“While some significant issues remain in contention, I am cautiously optimistic that they can be resolved in the upcoming 30-day extension period,” he said.

The terms of the royalty agreement were not announced.