The judge presiding over the hearing had previously issued a temporary restraining order that blocked the city from placing migrants at the former St. John Villa Academy.
The restraining order was later overturned by an appellate judge.
Opponents of the shelter presented arguments for a preliminary injunction on Thursday, but the judge presiding over the hearing decided not to rule on the case, saying it's a serious issue that needs to be analyzed.
Several dozen migrants are currently staying at the former school which has been met with protests by residents.
Opponents are arguing that the city has exceeded its authority and the shelter violates existing zoning laws and creates a nuisance.
The city's lawyer, Chad Hughes, argued in court that it is an unprecedented humanitarian crisis, saying in part, "we do not control the flow of the migrants into the city and when they are here, we have certain obligations, and we are doing our best to get them out of shelters so we don't have to continue building shelters."
Mayor Eric Adams has maintained the city is doing what it can to address the crisis and said it was "an embarrassment and insult" to say the city hasn't done enough for asylum seekers.
"NYC and the residents here should be applauded for what we have done, we have taken up the national crisis on our own, we've done a darn good job," Adams said.
He welcomed any creative ideas to get migrants to work, including state-issued work permits, which is an idea that Gov. Kathy Hochul entertained this week.
The plan would provide migrants with state-approved work papers as a potential workaround while thousands of asylum seekers wait for federal work authorization.
Adams said 110,000 asylum seekers have passed through New York City since April 2022 and the issue is creating a $12 billion budget deficit.
ALSO READ | Mayor Eric Adams says asylum seeker crisis 'will destroy New York City'
Mayor Eric Adams says asylum seeker crisis 'will destroy NYC'
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