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 that handle about 40 percent of all U.S. container cargo, a federal mediator announced today.

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 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 master contract between the International Longshoremen’s Association and the U.S. Maritime Alliance expired in September. The two sides agreed to extend it, but it had been set to expire again at 12:01 a.m. Sunday.

As recently as Dec. 19, the president of the longshoremen, Harold Daggett, had said a strike was expected.