The strike is now in its fourth day. Clerical workers from a chapter of the International Longshore and Warehouse Union walked off the job on Tuesday, and longshoremen are honoring their picket lines.
"We are not fighting for a pay raise. We are fighting to keep these jobs," said Kim Rich, ILWU office clerical unit.
But Stephen Berry of the Los Angeles/Long Beach Harbor Employers Association says no layoffs have been proposed.
"They've demanded that we replace positions that have been vacated by retired workers or workers who have left the workforce. These demands are unreasonable," Berry said.
Loading and unloading cargo ships have come to a virtual halt at the nation's busiest cargo complex. Los Angeles and Long Beach handle 40 percent of the nation's import trade. The employers said in a statement that the picketing has "harmful repercussions for tens of thousands of people whose livelihood in the port communities and beyond depends on the cargo moving through the ports."
"The 600 clerks involved in this strike -- the highest paid office clerical workers in America, and who have been offered absolute job guarantees and compensation boosts -- continue to put their own self-interests first," the statement said.
At least 18 cargo ships have been unable to load or unload since workers began the strike on Tuesday. Phillip Sanfield, Los Angeles port spokesman, said a handful of vessels that were anchored offshore left for other ports.
The clerical workers have been without a contract for two years. Contract talks resumed Thursday night. Berry remained hopeful about a resolution, saying the talks have been professional and courteous.
"There's a mutual commitment to go forward," Berry said. "The employers remain hopeful that there will be a quick resolution and we can get the cargo flowing again."
Workers intend to continue picketing until a contract is reached.
The Associated Press contributed to this report.