Four months after Gov. Andrew M. Cuomo announced a state of emergency on the New York City subway and three months after the Metropolitan Transportation Authority instituted an $836 million rescue plan, transit officials said they have slashed the time it takes to respond to emergencies, reducing the average 45-minute response time by about half with an eventual goal of driving that figure down to 15 minutes.

In data to be released this week, the transportation authority said it would show that it is working toward meeting year-end goals regarding inspections and repairs at key points in the vast system. Mechanical failures have also declined in recent weeks, though officials were unable to provide precise figures.

“Think of it like a patient that has suffered severe trauma,” said Joseph J. Lhota, the chairman of the transportation authority. The first thing that needs to be done is to stabilize the patient, he said, and stop the bleeding. But officials said the bigger aim by early next year was to return service to the pre-crisis level, which would require reducing the number of major incidents by 40 percent. A major incident is defined as a problem that causes the delay of more than 50 trains. At the height of the crisis, there were more than 80 major incidents on average a month.

Those efforts, however, Mr. Lhota warned, could be jeopardized by an ongoing fight with City Hall over funding. The state agreed to pay half the cost of the emergency plan and said the city should pay the other half. Mr. Lhota said if the city does not contribute, the agency would have to stop hiring new workers in January. Officials said that 764 workers have been hired and they want to hire at least 1,600 more.