Deputy Mayor Fabien Levy said the Adams administration is reviewing the state’s letter.

He added, “But because this is such a significant crisis, we need more, including more space around the state and a statewide order that bars localities from passing ordinances that prevent asylum-seekers from being relocated to other parts of New York State.”

Adams, meanwhile, said the city and state would continue to work together, refraining from criticizing Hochul’s efforts.

“We are really pleased with the relationship we have with this governor. Unlike some of the tension with other administrations, we —the governor and I — have constantly talked about our coordination,” Adams told reporters later Wednesday. “So if her observation is that here’s some things that you can do differently, we’re all in.”

Gay and her private law firm replaced Attorney General Tish James in representing the state after James took the unusual step to not defend the state, citing a philosophical difference over the state’s contention that a right-to-shelter regulation that requires housing for the homeless in the city doesn’t apply statewide.

The 12-page letter is Hochul’s response to requests that Adams formally made a week earlier for more state intervention in a letter obtained by POLITICO. The court fight is the first evidence of what appears to be a behind-the-scenes tussle between the city and state over how to handle the issue.

Adams and Hochul have stressed publicly that they are working collegially to address the problem as the city faces an overrun of its shelter system and as Adams has shipped migrants to other parts of New York — often to the disapproval of local leaders.

The document detailing state funding and resources for the support of migrants comes as pressure intensifies on the Hochul administration to do more for Adams’ team. The city’s shelter and emergency housing system has buckled under the weight of the nearly 100,000 migrants who have arrived since last spring.

Elected officials, community advocates and business groups have joined in a chorus of demands for more federal and state aid to the city, though the calls for President Joe Biden to expedite work authorization are by far the loudest.

In the state letter Tuesday, Gay also wrote, “Moreover, the City’s failure to inform the State of critical incidents that have occurred in shelters outside of the City has compounded these difficulties.”

The bulk of the state’s response was concentrated on what Albany has granted to City Hall to shelter and care for newcomers from the U.S.-Mexico border.

The newest state-run and state-funded emergency housing complex, on the parking lot of the Creedmoor Psychiatric Center in Queens, opened to migrant men Tuesday afternoon.

The letter also stressed an argument Hochul has made verbally: that the state doesn’t believe the law requiring shelter for those who need it applies beyond the five boroughs.

The public defenders and housing advocates who want an emergency hearing on the right to shelter law after migrants were forced to sleep on the streets earlier this month in midtown Manhattan urged the sides to come together.

“At this consequential time, we need both the State and the City, along with assistance from the Biden Administration, to work together constructively and in good faith,” members of the Legal Aid Society and the Coalition for the Homeless said in a statement Wednesday.