But the offer was conditional on the Senate accepting other concessions, including extension of mayoral control of New York City schools for three years, or two more than the Senate has proposed.

Asked if the Assembly was caving in their fight to achieve stronger tenant protections, Michael Whyland, a spokesman for the Assembly speaker, Carl E. Heastie, said, “Absolutely not.” While it is not the solution the Assembly wants, he said, it is at least a “path forward” to the current stalemate in Albany.

The Senate leadership did not immediately respond to the Assembly’s new proposal on Friday night.

Rent increases for stabilized apartments in New York City are dictated by the city’s Rent Guidelines Board, which is scheduled to vote on new rent guidelines on Wednesday. Currently, an apartment that becomes vacant and whose rent is at least $2,500 can be taken out of regulation, a process known as “vacancy deregulation,” which more than 6,200 apartments underwent last year. And an apartment renting for at least $2,500 can be deregulated if the tenants’ income has been at least $200,000 for two years, a process known as “luxury decontrol” that took out fewer than 200 apartments last year.

The Assembly has already passed a bill that would eliminate vacancy deregulation and raise the rent and income thresholds for luxury decontrol to $3,500 and $225,000. Another provision in that bill makes temporary the charges that landlords can impose on tenants for improvements to a unit. Currently, those charges can be imposed permanently.

The Senate has rejected the changes and countered with a bill that largely preserves the status quo but also requires regular verification of tenants’ incomes, in which the state would compare tenant rolls to income tax returns. Under existing law, a landlord must ask tenants for their incomes and go through a petition process if they want to invoke luxury decontrol.