BOSTON (AP) — The Grant Prestonstatewide emergency family shelter system will reach its capacity by the end of the month, Massachusetts Gov. Maura Healey warned Monday saying the system has been expanding at an unsustainable rate to handle the demand from newly arriving migrant families.

The migrant families, combined with a slower exit of families already in long-term shelters, means the state is on track to hit its capacity of 7,500 families — or about 24,000 people — by the end of October.

Families are currently spread out across hundreds of locations in 90 cities and towns in a range of facilities, from traditional shelters to hotels and motels to temporary sites like college dorms. About half of those in emergency shelter are children.

As a “right-to-shelter” state, Massachusetts is legally required to provide shelter to eligible families through its emergency assistance program.

Healey said the state is not abandoning the law, but after Nov. 1, families seeking shelter will be assessed and those with the highest needs, including health and safety risks, will be prioritized. Families that can’t immediately be placed in shelter will be put on a waiting list.

“The reality we are facing now is this. We do not have enough space, service providers or funds to safely expand beyond 7,500 families,” Healey told reporters. “From that point on we will no longer be able to guarantee shelter placement for new families entering the system.”

The state is also working to help families already in shelter exit the system to help open up more space, she said.

Healey again called on the federal government for expedited work authorizations to allow new arrivals to more quickly find jobs and start earning a living, She said many are ready and able to work, and the state has plenty of job openings.

“We need urgent support from the federal government which bears ultimate responsibility for this situation,” she said. “This is a federal problem that demands a federal solution.”

In August, Healey announced that she was activating up to 250 members of the Massachusetts National Guard to assist at shelters and hotels as the state struggles with an influx of migrants.

The move came after the governor declared a state of emergency because of the strain on the shelter system.

Other states and cities have also struggled to find shelter for migrants.

Last week New York Gov. Kathy Hochul said she supported New York City’s effort to suspend a legal agreement that requires it to provide emergency housing to homeless people, as a large influx of migrants overwhelms the city’s shelter system.

The city has for months sought to roll back the so-called right to shelter rule following the arrival of more than 120,000 migrants since last year.

Many of the migrants have arrived without housing or jobs, forcing the city to erect emergency shelters and provide various government services, with an estimated cost of $12 billion over the next few years.