A spokeswoman for the authority, Beth DeFalco, said that a piece of signal equipment from the 1930s, known as an interlocking, had failed at 34th Street on Tuesday morning. The emergency repairs that followed caused significant service disruptions.

“We apologize for this inconvenience and are working to improve service,” Ms. DeFalco said, noting that the signals and interlocking at 34th Street were being upgraded as part of the authority’s capital program.

Last month, the authority released a six-point plan to reduce subway delays, and Mr. Cuomo began a competition to find new ways to upgrade the signal system more quickly.

As the subway system reaches a crisis point, the authority has not had a permanent leader since January. It is not clear if Mr. Cuomo will appoint a new chairman and chief executive to run the agency before the current legislative session ends on Wednesday.

On Monday night, the State Senate confirmed seven people to serve on the authority’s board, including two new members: Scott Rechler, a former vice chairman at the Port Authority of New York and New Jersey, and Carl Weisbrod, a former chairman of the New York City Planning Commission. Mr. Cuomo recommended Mr. Rechler to the board, and Mayor Bill de Blasio recommended Mr. Weisbrod.

But on Tuesday afternoon, Mr. Cuomo pressed for even greater control over the authority’s board. Mr. Cuomo, who already controls six board seats and names its chairman, said he would advance legislation that would allow him to appoint two additional board members to consolidate his power over the agency.

The board typically has 17 voting members, including four members recommended by the mayor; three delegates from Westchester, Nassau and Suffolk Counties; and four suburban members who share one vote from Orange, Dutchess, Rockland and Putnam Counties. In 1983, the governor’s father, Mario M. Cuomo, tried unsuccessfully to add three members to the board to attain a majority.