Massachusetts has begun awarding grants to local agencies to set up temporary housing sites for homeless families as officials grapple with finding newly arriving migrants places to stay after hitting a state-imposed limit of 7,500 families in the state’s emergency homeless shelter system.

Catholic Charities Boston is the first organization to be awarded a grant to provide temporary rooms to extremely low-income families with children and pregnant individuals, the United Way of Massachusetts Bay announced this week.

The grant will pay for a site in the greater Boston area that opened on Tuesday evening and can accommodate up to 27 families, or about 81 people, as they wait to enter the state’s emergency shelter system, officials said.

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Catholic Charities Boston will provide bedding, meals, staff, and security. The site is available to families eligible for the the state’s family shelter system but who could not be immediately placed in a shelter.

Democratic Gov. Maura Healey announced the $5 million grant program earlier this month.

Sarah Bartley of the United Way said the agency has already received several other grant applications. The grants are meant to support community gathering spaces with restrooms and heat, such as places of worship, community centers, and school buildings, to provide safe space for families to find short-term, congregate shelter, meals and other basic necessities, she said.

The flexible program will remain in place through the winter and spring, officials said.

On Monday, the state began letting homeless families stay overnight in the state transportation building in Boston. The space in the office building is large enough to provide overnight shelter for up to 25 families with cots and limited amenities and will only be used in the evening and overnight hours, officials said.

The space will be available to families determined eligible for emergency assistance and is expected to operate for about two weeks until additional safety net shelter sites are operational.

The spike in demand is being driven in part by migrant families entering the state. About half of the current shelter caseload are new arrivals to Massachusetts, according to the Healey administration.

As of last Friday, there were 92 families on the state’s waiting list for emergency shelter.