Keeping the state’s emergency shelter system from buckling under continued high demand could cost Massachusetts $900 million next fiscal year, according to state officials. But they say they have a plan to pay those bills without making budget cuts elsewhere.

A law Gov. Maura Healey signed two weeks ago poured another $250 million into the family shelter network, which has stretched beyond its capacity amid an influx of new migrant arrivals over the past several months. That law also required Healey’s administration to report spending details and other shelter data regularly to lawmakers.

Administration and Finance Secretary Matt Gorzkowicz and Housing and Livable Communities Secretary Ed Augustus filed the first report Monday.

They told legislative budget writers that the recently approved shelter money will keep the system running "for the next several months," and that Healey will soon be asking for more funding "to avoid imminent run-out dates for key programs."

The administration plans to use $700 million stashed in a surplus state revenue account to cover shelter costs and related needs for the rest of this fiscal year and much of the next one, which begins in July. Along with direct shelter expenses, a portion of that money would go toward housing production and preservation efforts.

It's unclear what lawmakers will make of the plan. Senate Ways and Means Chairman Michael Rodrigues declined to weigh in, and an aide to House Ways and Means Chairman Aaron Michlewitz did not respond to a request for comment Tuesday.

Massachusetts Taxpayers Foundation President Doug Howgate said state officials put those surplus dollars aside in good financial times.

"Applying those to this to help buy some time to manage through this challenge, I think makes some sense," he told GBH News. "What's critical, though, is as we do this, we have to actually come up with a plan as well for how to manage this program going forward, because clearly this is not a sustainable financial solution. It's also not a sustainable policy or kind of humanitarian solution."

As of Tuesday, a total of 7,529 families across Massachusetts were enrolled in the shelter system, including 10 who entered shelter in the past day.

An estimated 3,516 families in shelter as of Dec. 12 were migrants, refugees or asylum seekers, according to the report, accounting for a little less than half the system's total capacity. Of those new arrivals, 813 individuals were authorized to work in the United States.

Healey and other Massachusetts policymakers have pressed the Biden administration to speed up the work authorization process as a way to help families move out of shelter and into permanent housing. A work authorization clinic state and federal officials hosted in Reading last month helped 2,910 people, the report said, including 1,031 adults and children who received seasonal vaccinations there.

The report also breaks down how many families are staying in shelters, hotels and motels across the state through the emergency assistance system. The greatest number — 1,308 families — are staying in Boston, while Melrose, Stoneham and Hanson are hosting one family each.