SAN DIEGO — Leaders of labor unions representing roughly 800,000 workers in Los Angeles County recommended Monday that the Los Angeles Federation of Labor officially sanction a potential strike at grocery stores across Southern California, including San Diego County.

The sanction, if approved by the federation's executive board, would mean that workers represented by 300 labor unions would honor picket lines and refuse to shop at Ralphs, Vons and Albertsons stores.

"If workers are forced to go on strike, our members and their families will not cross the picket line," said Rusty Hicks, president of the Los Angeles County Federation of Labor.

RELATED: San Diego grocery workers approve power to strike

Last week, grocery workers across Southern California overwhelmingly authorized its union -- United Food and Commercial Workers -- to call a strike if a contract agreement with the companies cannot be reached. If a strike happens, it would be the first grocery walkout in the region in nearly 16 years.

"Southern California grocery workers voted in large numbers, and overwhelmingly rejected the unfair terms that have been proposed by Ralphs, Albertsons and Vons," John Grant, president of United Food and Commercial Workers Local 770, said last week.

Albertsons/Vons/Pavilions issued a statement saying, "The outcome of the strike authorization vote does not change anything related to this process. We remain committed to negotiating a contract that is fair to all parties, including our employees, and will continue to work to achieve that."

Ralphs issued a similar statement and said, for now, "it is business as usual in Ralphs stores."

The strike authorization vote means union negotiators have the power to call for a strike, if deemed necessary, but it does not automatically mean a walkout will occur.

The next bargaining sessions involving the union and the companies are scheduled for July 10, 11, and 12, Grant said.

The contract between the union and the companies expired in March. That pact was approved by workers in 2016 and included annual raises for most workers, along with increased pay for entry-level cashiers and concessions on holiday pay and retirement age, union officials said at the time.

On Wednesday, union officials said the most recent contract offer made by the grocery companies included wage increases of less than 1% and nearly 25% cuts in cashier wages.

The labor dispute raises fears of a repeat of the 2003-04 Southland grocery strike that dragged on for 141 days. That work stoppage was estimated by some analysts to have cost the supermarket chains as much as $2 billion, with locked-out workers losing $300 million in wages.