The chairman of the Metropolitan Transportation Authority on Wednesday sought to reassure New Yorkers that the agency would secure the necessary funding to forestall what transit experts were warning about — a slump in service, overflowing subway trains and more frequent delays.

The sense of alarm has been occasioned by a $15 billion gap in the agency’s five-year capital plan, which is meant to finance long-sought repairs and improvements to the city’s transit system.

Transit officials and elected leaders are currently in discussions about how to fill that gap or, alternatively, to pare down costs.

But the authority’s chairman, Thomas F. Prendergast, warned that future stages of major construction plans and renovations for the overtaxed system were at risk if officials were unable to come to an agreement. The full five-year plan calls for $32 billion.