At a meeting in the East Village, the board voted 5-4 to propose increases of 0.5 percent to 2.5 percent on 1-year leases and 1.5 percent to 3.75 percent on 2-year leases.
Angry tenants held a rally before the meeting to express their opposition.
A series of hearings will now be held in all five boroughs, to give tenants and landlords a chance to testify.
A final vote on possible rent increases will be held June 27.
Last year, the board approved hikes of 1.5 percent on one-year leases and 2.5 percent on two-year leases.
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