The city’s already-flailing shelter system is cracking amid the flood of migrants to the Big Apple — committing what homeless-rights activists are calling its worst failure to provide services in more than a decade.

Sixty men seeking shelter were out of luck Monday night when the city’s Department of Homeless Services failed to find them a place to stay, the first violation of the Big Apple’s court-ordered right-to-shelter rule for single adult males in 13 years, a rep for Legal Aid told The Post.

It also was the second time DHS  failed to provide beds in recent weeks — as the city struggles to handle the nearly 10,000-and-counting migrants who have been arriving from the US southern border since the summer began.

About 7,300 of those migrants are currently in the city’s shelter system, Big Apple officials told The Post on Tuesday.

“That’s a significant number — that would have a significant impact on the shelter system,” former City Councilman Stephen Levin,  the longtime former head of the council’s General Welfare Committee, noted of the tidal wave of migrants.

“You also have increases in rents around the city, the [COVID] eviction moratorium lifted,’’ he said, referring to issues putting additional strain on the homeless system.

The number of people in New York’s shelter system had swelled to 55,485 as of Monday.
That was up almost 25 percent from the 45,844 people reported on the same day in May, when officials say the migrant surge began.

The tally is still far below its all-time high reported in January 2019, when the city’s homeless figure hit 61,415.

But Legal Aid and the Coalition for the Homeless said in a joint statement on the current saga, “It is now clear that this Administration simply does not have a handle on the city’s sprawling homelessness crisis and the serious capacity issues in the Department of Homeless Services’ (DHS) shelters.

“We are extremely alarmed … and, as legally required, the City must immediately promulgate a plan to ensure that no further violations occur,” the groups said.

“Should the City continue to deprive our clients of this codified right, we’ll seek action from the court.”

The last violation  involving homeless single men occurred in 2009 during the administration of then-Mayor Michael Bloomberg.

The dismal development is a black eye for the city’s embattled social-services commissioner, Gary Jenkins, who The Post previously revealed was vacationing as his agencies missed their own deadlines to secure additional shelter and intake capacity to better manage the crisis.

Jenkins oversees both DHS and the city’s Human Resources Administration.

The city also wracked up another violation in July, during the early weeks of the migrant surge, when DHS left recently arrived families with children stuck in its Bronx intake facility overnight after failing to provide them beds.

That disclosure came after  allegations that top DHS officials ordered the agency’s staff not to inform City Hall of the woes.

The last time the city’s right-to-shelter requirements were violated for families was in 2014.

A spokeswoman for DHS did not dispute the claims from Legal Aid and the Coalition for the Homeless but said in a statement, “Our teams remain committed to working around the clock while quickly adapting to the reality on the ground and identifying additional capacity to make sure that we are providing supports to anyone in need of shelter services regardless of background and immigration status.”