Mayor Bill de Blasio plans to push for a tax on wealthy New Yorkers to pay for improvements needed to address the crisis engulfing New York City’s subway, city officials said on Sunday.

The proposal is the latest move in the battle between Mr. de Blasio and Gov. Andrew M. Cuomo over who bears responsibility for repairing the deteriorating transit system. The plan would also pay for half-price MetroCards for low-income riders — part of a national movement that has gained momentum in New York.

Mr. de Blasio will announce a so-called millionaires tax on Monday for wealthy New York City residents to pay for subway and bus upgrades and for reduced fares for more riders, an idea that has been successful in Seattle.

His funding push comes as the subway faces a multitude of problems, and leaders at the Metropolitan Transportation Authority, which operates the subway, have called on Mr. de Blasio to provide more money for the system.