"I'm hopeful that the mediator will be here today. We've got to get a deal and get a deal as soon as possible," Villaraigosa said Tuesday at a news conference.
About 800 members of the International Longshore and Warehouse Union Local 63 have been on strike since Nov. 27, shutting down 10 of 14 cargo terminals at the ports in Los Angeles and Long Beach, Calif.
The strike has effectively halted cargo container unloading, as 10,000 members of the ILWU have refused to cross picket lines.
All told, the Los Angeles Times reported Tuesday, 600,000 jobs are affected by the strike.
The union members contend port management has been outsourcing jobs, moving clerical work to other areas where labor is cheaper.
Employers, however, say they have offered the union a generous compensation package and full job security.
The union says employers are downsizing union jobs through attrition.