(Corrects headline to insert dropped word "in")

By Joseph Ax

PRINCETON, New Jersey (Reuters) -New Jersey's commuter rail engineers walked off the job early on Friday after marathon contract talks stalled ahead of a midnight deadline their union set for meeting its wage demands, igniting the first strike to engulf the third-largest U.S. transit system in more than 40 years.

The strike, expected to idle trains serving hundreds of thousands of daily passengers in New Jersey and New York, came into effect at 12:01 a.m. EDT (0401 GMT) on Friday.

NJ Transit said its rail system was commencing "a safe shutdown" at 12:01 a.m., with no new departures started after that point, though trains already en route would finish their trips.

The Brotherhood of Locomotive Engineers and Trainmen, which represents 450 NJ Transit engineers who drive the agency's commuter trains, said a 15-hour, nonstop bargaining session on Thursday broke off when management negotiators walked out of the talks at 10 p.m..

The union strike declaration came as New Jersey Governor Phil Murphy and NJ Transit's Chief Executive Officer Kris Kolluri held a news conference. They told reporters talks had paused but that management remained willing to resume negotiations at any time.

"We must reach a final deal that is both fair to employees and affordable," Murphy, a Democrat, told reporters. "Let's get back to the table and seal a deal."

Murphy and Kolluri said the U.S. National Mediation Board had reached out to both sides to propose reopening talks on Sunday morning, or sooner if the parties wished.

The union statement made no mention of when talks might be restarted. It said picket lines would go up at 4 a.m. at several locations across the rail system, including NJ Transit's headquarters in Newark, Penn Station in New York City, and the Atlantic City rail terminal.

The governor and the NJ Transit CEO also outlined contingency plans for dealing with the work stoppage, the first transit strike to hit New Jersey since a three-week walkout in 1983.

WORKERS URGED TO STAY HOME

The looming strike had already prompted the agency to cancel trains and buses to MetLife Stadium for pop star Shakira's concerts on Thursday and Friday nights.

In an advisory, NJ Transit encouraged commuters to work from home starting on Friday if possible.

The agency said it would increase bus services on existing lines and charter private buses to operate from several satellite lots in the event of a rail strike but warned buses would only be able to handle around 20% of rail customers.

The labor clash came weeks after negotiators had agreed on a potential deal in March, but the union's members voted overwhelmingly to reject it.

The union has said it is simply aiming to raise the engineers' salaries to match those at other commuter railroads in the region.

NJ Transit has said it cannot afford the pay raises that the engineers are seeking because 14 other unions that negotiate separate labor contracts with the agency would demand the same, higher wage rates for their members.

NJ Transit says the engineers currently make $135,000 on average and that management had offered a deal that would yield an average salary of $172,000. But the union has disputed those figures, saying the current average salary is actually $113,000.

The parties have exchanged accusations of bad faith bargaining.

Kolluri said last week that the union was "playing a game of chicken with the lives of 350,000 riders."

"We have sought nothing more than equal pay for equal work, only to be continually rebuffed by New Jersey Transit," Tom Haas, the union's general chairman, said earlier this week.

(Reporting by Joseph Ax in Princeton, New Jersey. Additional Reporting and writing by Steve Gorman in Los Angeles; Editing by Lincoln Feast.)