The subway system has shown signs of improvement in recent months for the first time in nearly six years, with on-time performance climbing to over 80 percent. But subway leaders say elevating it to a 21st-century system will require an overhaul of the subway’s aging signals — and tens of billions of dollars.

Transit advocates have argued that the cost of additional police would be better spent on those upgrades or, as an example, increasing subway service on weekends.

“More frequent trains would mean shorter waits and less crowding, making the subway even safer,” said Danny Pearlstein, the communications director for The Riders Alliance, a transit advocacy group, in a statement.

The overall number of violent crimes has decreased so far this year compared with last year. But certain crimes, like robberies, are on the rise and some regular riders have complained that they feel less safe riding subways outside of rush hours than they have in recent years.

“Folks who are saying we don’t need more police should imagine making that argument to one of the three people who were raped or to the people who were groped on the subway this year,” said Sarah E. Feinberg, an M.T.A. board member. “If they are thinking about it from this perspective, they wouldn’t say it isn’t worth investing in protecting people or preventing the next assault.”

Mr. Cuomo has repeatedly defended the need for more police officers, arguing that riders will be leery of riding the trains, no matter how good service is, if they perceive them to be dangerous.

“The trains have to run on time and they have to be safe,” the governor said recently. “You have to accomplish both. It is not one or the other.”