WASHINGTON — Federal mediators seeking to avoid a walkout of thousands of dockworkers, including those in the Charleston area, have called a meeting of them and shipping companies.

The Federal Mediation and Conciliation Service said that Director George Cohen called the meeting of the International Longshoremen’s Association and the U.S. Maritime Alliance before the midnight Saturday expiration of the contract extension. It said Monday the parties have agreed to attend the meeting but wouldn’t elaborate.

Talks between the dockworkers and the shipping companies broke down Dec. 18, just weeks after a critical West Coast port complex was crippled by a strike involving a few hundred workers. Issues including wages are unresolved, but the key sticking point is container royalties, which are payments to union workers based on cargo weight.

Port operators and shipping companies, represented by the Marine Alliance, want to cap the royalties at last year’s levels. They say the royalties have morphed into a huge expense unrelated to their original purpose and amount to a bonus averaging $15,500 a year for East Coast workers already earning more than $50 an hour.

The longshoremen’s union says the payments are an important supplemental wage, not a bonus.

The union represents 14,500 workers at more than a dozen ports extending south from Boston and handling 95 percent of all containerized shipments from Maine to Texas.

Retailers fear another strike could have catastrophic effects and have asked President Barack Obama to intervene.

The National Retail Federation wrote to Obama last week and asked him to use “all means necessary” to head off a strike.