Landlords, potential tenants and housing advocates said they were encouraged by the changes, which must be announced in the city register and opened for public comment before taking effect in the fall.

Kevin Jones, 55, said he has had a voucher from Living in Communities IV, or LINC IV, for three years and has not been able to find an apartment to rent.

“Someplace semi-decent? It’s really hard to get,” said Mr. Jones, who said he was a carpenter before he became disabled and then homeless.

He said he still believes the rent rates need to be raised even higher to lure landlords who are unwilling to participate in voucher programs.

Frank Ricci, director of government affairs for the Rent Stabilization Association, a landlord organization, said many landlords were left with tenants who could not pay the rent after a program called Advantage, which predated the de Blasio administration, folded after the city and New York State cut funding.

Mr. Ricci, whose group represents about 25,000 landlords, said the city should consider all costs incurred by landlords when looking at rent rates. A large family can generate a high water bill, Mr. Ricci said. “Most owners pay more in water than fuel,” he said. “You can never talk about the income side without talking about the expense side of the equation.”

It is against the law for landlords with buildings of six or more units to refuse vouchers.

Last year, the city created a unit to crack down on landlords, and last month, the unit filed lawsuits against the manager of an apartment complex on Staten Island and a real estate broker who rented apartments in two Bronx buildings because they would not accept tenants with vouchers.