Just days after state legislators agreed to extend rent regulations for another four years, New York City’s Rent Guidelines Board is scheduled to vote on Monday evening on whether to increase rents for more than one million rent-stabilized apartments.

The board, which voted for its lowest-ever rent increases last year, has a chance to make history again. It is considering freezing rents for the next year. The board has never voted for no increases.

The vote, to be held at Cooper Union’s Great Hall in Manhattan, will be the first test of a rent board appointed entirely by Mayor Bill de Blasio. The mayor asked for a rent freeze last year, when a majority of the board were de Blasio appointees, along with some holdovers from the Bloomberg administration. But the board, which consists of two tenant representatives, two landlord representatives and five members of the public with experience in housing, finance or economics, resisted the mayor’s call.

Instead, the board passed the lowest increases since it was established in 1969 — up to 1 percent for one-year leases and 2.75 percent for two-year leases.