It comes as Mayor Eric Adams continues to make clear that he will not turn them away.
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Catholic Charities of the Archdiocese of New York says more than 1,500 migrants have shown up their doors just in the last six weeks alone, and they -- along with the city -- are helping with things like food, places to stay, legal help and health care.
"These just aren't cases, these just aren't problems, these just aren't statistics, these are not just refugees and asylum seekers in the plural," Dolan said. "These are people with names, and with dads and moms."
Catholic Charities is facing an unprecedented influx in asylum seekers, and Dolan expressed the magnitude of the situation following the meeting.
"They've just been through turmoil," he said. "Some of them, for months, have been walking from Colombia and Venezuela."
It has been a long and difficult journey for families, like Maria and her 8-month-old son, who spent days traveling from Venezuela.
Catholic Charities has worked to get migrants basic necessities, any legal help, and assistance connecting them to family members who are already in other parts of the country.
Some are calling this a political stunt and a move that has strained both the relationship between Texas Governor Greg Abbott and Adams as well as New York City's resources.
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Adams, however, says the city will do what it can to help.
It's unclear when this influx will die down, because the buses have been arriving at the Port Authority unannounced.
City officials estimate that about 2,800 asylum seekers have arrived so far by bus from Texas and Arizona.
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Adams has asked for federal funding to help with the influx and he says he's hopeful it will happen.
RELATED | New York City Council holds special hearing on asylum seekers bused from Texas
NYC holds special hearing on asylum seekers bused from Texas
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