(Reuters) - New Jersey Transit trains will begin operating again on Tuesday after the agency reached a deal with striking rail engineers on wage increases, ending a work stoppage that affected about 350,000 passengers.

The statewide rail strike, the first to hit NJ Transit in more than 40 years, had begun just after midnight on Thursday, leaving tens of thousands of commuters to New York scrambling to find alternate transportation.

The Brotherhood of Locomotive Engineers and Trainmen union, which represents 450 NJ Transit engineers who drive the agency's commuter trains, said it reached an agreement on pay with the agency on Sunday and that its members would return to work on Tuesday. The union had previously said that train service would resume on Monday.

Details of the deal were not immediately released. The agreement will be put to a vote of the union's members, who rejected an earlier deal last month.

"The only real issue was wages and we were able to reach an agreement that boosts hourly pay beyond the proposal rejected by our members last month and beyond where we were when NJ Transit's managers walked away from the table Thursday evening," Tom Haas, the union's NJ Transit chairman, said in a statement.

NJ Transit, the third-largest transit system in the U.S., provides more than 700,000 passenger trips a day on average across its train, light rail and bus lines.

The two sides had blamed each other for the walkout, after last-minute talks on Thursday broke down without an accord.

Murphy and NJ Transit officials had said the agency could not afford to meet the union's pay demands, while the union had said it was simply aiming to bring its members' salaries in line with those of engineers at other commuter systems in the region.

(This story has been corrected to say that the service will resume on Tuesday, not Monday, after the union corrected its earlier statement, in paragraphs 1 and 3)