The clerks overwhelmingly rejected a contract offer Friday by the chains Kroger Co.'s Ralphs, Safeway Inc.'s Vons and Albertsons Inc. and authorized a walkout.
The mediator met with negotiators from the chains and the United Food and Commercial Workers union Friday and worked into the night. The groups arranged for additional talks Saturday, a union official said.
If talks fail, the union planned to target one of the three supermarket chains for a strike and to ask the companies not to lock out workers from the other two. Union officials did not reveal which chain would be targeted.
"I guarantee you that we will win this strike as long as we have the support of consumers and as long as we have the support of the Teamsters," said Rick Icaza, president of the UFCW Local 770 in Los Angeles and one of the negotiators.
The chains, which make up 60 percent of the Southern California market, operate nearly 900 stores from San Luis Obispo to San Diego with employees covered by the union. The last time the grocery workers went on strike was 1978 and it lasted less than a week.
"We believe any call to authorize a strike is premature and regrettable," said Terry O'Neil, a spokesman for Ralphs.
Negotiations between the union and the chains ended Sunday, and the contract covering the grocery clerks has since expired.
After weeks of negotiating, both sides were still at odds over several key issues, especially proposed changes by the companies to the scope and cost of employees' health care coverage.
The union called on Southern Californians to honor picket lines and shop elsewhere.
"We are your friends, we are your neighbors, we are your local supermarket workers who serve you every day," said Connie Leyva, president of UFCW Local 1428, which covers the San Gabriel Valley. "Please support our strike."