The Metropolitan Transportation Authority is rushing to finish the long-delayed Second Avenue subway this month, but officials at a board meeting Monday once again did not announce an opening date, with less than three weeks left to meet their deadline, Dec. 31.

Under pressure from Gov. Andrew M. Cuomo, officials at the authority said that workers were making progress at three new stations on the Upper East Side of Manhattan but that they still had to complete a series of tests to make sure the stations would be ready for subway riders by Dec. 31. Mr. Cuomo, a Democrat who controls the authority, was “cautiously optimistic” that the deadline would be met, his office said.

Thomas F. Prendergast, the chairman of the authority, echoed those comments at a board meeting on Monday, saying he was also “cautiously optimistic,” but he did not give an opening date for the line. Workers have finished installing elevators and escalators at the stations, and the final tests were scheduled to be completed by Dec. 23, officials from the authority said.

After nearly a century of planning and discussion, the Second Avenue subway line will start as an extension of the Q line, with three new stations at 72nd, 86th and 96th Streets. The first phase, which cost about $4.4 billion to build, will be the most ambitious expansion of New York’s subway system in a half-century. It is expected to ease overcrowding on the Lexington Avenue line, one of the city’s most congested routes.