The strike, called by the two largest unions representing Bay Area Rapid Transit system workers, will force hundreds of thousands of people to scramble to find alternate transportation for their Friday commute.

For the last week — since a 60-day cooling off period ordered by Gov. Jerry Brown ended on Oct. 10 — negotiators had been working long hours trying to resolve their differences. Strike deadlines were set by the union, then postponed, then set again. Anxious commuters — the railroad carries 400,000 passengers each day — stayed up late to find out whether trains would be running the next day.

But on Thursday, union leaders and BART managers, their frustration evident, emerged bleary eyed from 28 straight hours of negotiation to say they had failed to reach a deal.

“I’m surprised and sorry to be standing here tonight,” said Pete Castelli, executive director of the Service Employees International Union 1025. “In all my years in the labor movement, I’ve never seen an employer drive negotiations that were this close to a deal into a strike.” The service employees union and the Amalgamated Transit Union Local 1555 together represent 2,400 train operators, station agents, mechanics, clerical workers and other employees of the transit system.

Mr. Castelli and other union representatives said that the unions had compromised on pensions and health care and were close to an agreement on wages. But the talks broke down, they said, over how to handle disputes over work rules. An offer by the unions to refer those issues to an arbitrator whose decision would be binding was turned down by management, the union leaders said.

Tom Radulovich, the president of BART’s board of directors, said that it was their negotiating team who were “very, very surprised today when the unions walked out and said they weren’t going to talk to us anymore.”

“There is no need for them to strike,” Mr. Radulovich said of the unions.

Mayor Edwin M. Lee of San Francisco, who canceled a planned trip to China because of the impending strike, issued a statement late Thursday saying that a strike would harm the region’s economy and cause hardship for riders.

“I join Governor Brown in urging BART union and management leaders to return to the bargaining table and continue to negotiate in good faith to avoid a BART strike,” he said.

Oakland’s mayor, Jean Quan, also released a statement, endorsing the unions’ call for an arbitrator and urging BART to “reconsider and allow these negotiations to move into arbitration for the unresolved work rules issues.”

Over the past week, a parade of elected officials, including Lt. Gov. Gavin Newsom, have visited the labor talks, pleading for compromise to avert a strike. The federal government’s top mediator, George H. Cohen, director of the Federal Mediation and Conciliation Service, flew in from Washington to help with the talks.

But on Thursday, Mr. Cohen, who in 2011 helped resolve the National Basketball Association labor dispute, said he and his staff were heading home. While significant progress had been made, he said, in the end, “The parties were unable to bridge the gap.”

“Our effort to help them do that was not successful,” Mr. Cohen said.

On Sunday, BART managers presented what they said was their “last, best and final” offer and asked the unions to take it to their membership for a vote. That offer included a 3 percent annual wage increase, a 1 percent annual increase in employee contributions to pensions and an increase of 9.5 percent over the life of the four-year contract in employee contributions to health benefits. On Thursday, BART’s general manager, Grace Crunican, said that offer was still on the table.

On average, train operators and station agents earn more than $70,000 in salary and overtime annually, according to BART. Under the previous contract, transit system employees contributed $92 monthly for health benefits and paid nothing toward their pensions.

Many Bay Area residents have shown increasing impatience with the unions, and the news that BART employees would finally strike elicited more than a little anger, with some riders saying they felt they were being held hostage.

“As a fed employee that was just given hope again, I say be glad you have jobs and go to work. Stop this nonsense!” one man said in a Twitter message.

But others said they supported the unions even though they would be inconvenienced by the strike.

Although the rush hour promised to be nightmarish on Friday, with the strike adding hundreds of cars to the normal gridlock traffic on the Bay Bridge, the disruption could have been even worse. Governor Brown on Wednesday stepped in to head off a strike by employees of the East Bay’s bus system, Alameda-Contra Costa Transit, whose buses were relied on heavily in July, when BART employees walked out for four days. Governor Brown ordered a seven-day strike delay while a panel investigates the labor disagreement.