OAKLAND, Calif.—San Francisco's Bay Area Rapid Transit warned riders that the trains may not run Monday after two of the agency's largest union walked away from the bargaining table hours before a midnight deadline.

The agency has not received official word from the unions about a strike, but it must caution riders that a strike may begin after the end of Sunday night's regularly scheduled service, BART spokesman Rick Rice said in a statement.

He urged the unions to resume contract talks, noting that all parties had agreed on several issues when they returned to the bargaining table Sunday afternoon in an 11th hour attempt to avoid a walkout.

"We should use that momentum to reach a deal," the statement said.

Calls to the representatives from Service Employees International Union Local 1021 and Amalgamated Transit Union Local 1555 were not immediately returned.

A strike would cripple the region's Monday morning commute. Transportation officials say another 60,000 vehicles could be on the road, clogging highways and bridges throughout the Bay Area.

The unions' contracts are set to expire at midnight.

As the deadline neared, both sides said they were far apart on key sticking points including salary, pensions, health care and safety. Anticipated around-the-clock negotiations had fallen apart Saturday as the unions packed up and left after talks stalled amid claims that the parties met face-to-face once in 36 hours.

Sunday's last-ditch talks also came after Gov. Jerry Brown's secretary of the Labor and Workforce Development Agency, Marty Morgenstern, requested the parties continue negotiating to prevent a work stoppage of the nation's fifth-largest rail system.

"Our team is not encouraged by BART's proposal, but we are going to bargain at the request of the labor secretary in good faith as we have all along," said Josie Mooney, an SEIU chief negotiator. "But if BART continues to do 'surface bargaining,' then we will not come to an agreement."

Brown spokesman Evan Westrup said Sunday that the governor will not call for a "cooling off period at this time" as state mediators will continue assisting the negotiating parties.

"BART and its labor unions owe the public a swift resolution of their differences," Westrup said. "All parties should be at the table doing their best to find common ground."

The two unions, which represent nearly 2,400 train operators, station agents, mechanics, maintenance workers and professional staff, want a 5 percent raise each year over the next three years.

BART said that train operators and station agents in the unions average about $71,000 in base salary and $11,000 in overtime annually. The workers also pay a flat $92 monthly fee for health insurance.

Rice said BART's latest proposal offered a total of an 8 percent salary raise over the next four years, instead of its original offer of a total of 4 percent over the same period. The proposed salary increase is on top of a 1 percent raise employees were scheduled to receive Monday, Rice added.

The transit agency also said it offered to reduce the contribution employees would have to make to their pensions, and lower the costs of health care premiums they would have to pay.

Rice said Sunday that BART's latest proposal may not be its best last offer.

"We need to have some substantial discussions," Rice said. "I hope we can make some progress."

BART's last strike lasted six days in 1997. The transit agency handles more than 40 percent of commuters coming from the East Bay to San Francisco with the Bay Bridge handling another 50 percent said John Goodwin, a spokesman for the Metropolitan Transportation Commission.

Goodwin said commuters should consider carpooling, taking extra buses or ferries available and working from home if the trains stop. And, if commuters must drive to work, leave earlier or even later than usual, he said.

"We simply don't know what the status is," Goodwin said. "Unfortunately, we have to go with the assumption that BART will not be in operation."

Meanwhile, commuters such as Richard Graham, 43, of Pleasant Hill who works as a hotel banquet manager in downtown San Francisco, is left pondering his options, including a three-hour drive to work.

"I can't stop thinking about it," Graham said Sunday as he got off a train. "It would make take me 2 1/2 to 3 hours if I drive in to work. Then I've got to find parking, and that might cost me another 40 bucks, if there are any spots left."