Josie Mooney, a negotiator for the Service Employees International Union Local 1021, said there was “a 95 percent chance” that her union and members of the Amalgamated Transit Union Local 1555 would strike, after contract talks stalled Saturday.

“I’m afraid I don’t see a way we will avoid a strike,” she said after union leaders left the negotiating table Saturday, claiming they have met with BART’s management for only 10 minutes in the past 36 hours. The two unions represent nearly 2,400 train operators, station agents, mechanics, maintenance workers and professional staff.

A walkout could derail the more than 400,000 riders who use the nation’s fifth-largest rail system and affect every mode of transportation, clogging highways and bridges throughout the Bay Area. Such a strike could begin Monday after contracts expire at midnight Sunday.

BART spokesman Rick Rice said Sunday that the agency planned to attend talks scheduled for 1 p.m. and hoped union representatives would be there.

“We’re certainly expecting to have conversations today,” Rice said. “We’ll be there.”

Mooney said Saturday that the unions have no plans to meet with BART.

Negotiations between BART and the unions had intensified as Sunday night’s deadline loomed. Two state mediators were facilitating the negotiations, with each side seated in separate rooms.

As the parties went back to the bargaining table Saturday in Oakland for anticipated around-the-clock sessions, both sides said they were far apart on key sticking points including salary, pensions, health care and safety.

The unions want a 5 percent annual raise over the next three years. BART said Saturday 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 an 8 percent salary raise over the next four years, instead of its original offer of 4 percent. 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.

On Friday, the ATU asked California Gov. Jerry Brown to issue a 60-day “cooling off” period if no deal can be reached by Sunday’s deadline, but the SEIU and BART officials have urged Brown not to issue such an order.

The governor’s office has declined to comment.

BART’s last strike lasted six days in 1997. On Friday, other area transit agencies urged commuters to consider carpooling, taking buses or ferries, working from home and, if they must drive to work, to leave earlier or even later than usual.

“The bottom line is that a BART strike will be an absolute nightmare for everyone,” said Jim Wunderman, president and CEO of the Bay Area Council, a business advocacy organization. “Our transportation system simply does not have the capacity to absorb the more than 400,000 BART riders who will be left at the station. There will be serious pain.”