Migrant families are officially on a 60-day notice to find alternate housing.
The Adams administration says migrants will meet with case workers during the 60 days to work on the next leg of their asylum journeys.
Council Member Pierina Sanchez argues the city has not prepared for the move and says City Council voted to create more space in shelters by expanding housing vouchers. That goes into effect Wednesday.
Sanchez also says the city is not receiving enough assistance from the state.
Mayor Eric Adams imposed the 60-day limit in October for homeless migrant families, saying the move was necessary to relieve a shelter system overwhelmed by asylum-seekers crossing the southern U.S. border.
The Adams administration has warned for weeks that no one seeking a new placement is guaranteed another bed.
Adams and other city officials said Monday that they would prioritize families and try to place them near their children's schools in order to minimize any disruption to their education.
AP wires contributed to this story.