A Fort Point office building opening this week as an overflow shelter site for migrants will put emphasis on preventing families from “sleeping at Logan Airport,” according to its operator, the United Way of Massachusetts Bay.

The new 80-bed safety-net site in the ritzy Seaport neighborhood will be the second facility to open this year in Boston for migrant families that have taken refuge at the airport, weeks after the state converted a Roxbury recreation center into a shelter.

A conservative fiscal group says the situation is illuminating how the Healey administration has mismanaged the migrant crisis and is calling on the governor and top lawmakers to consider reforms to the state’s overburdened emergency assistance shelter system.

“Logan airport should be a secure location for people to travel, not a place for the Healey administration to use as temporary migrant housing,” said Paul Diego Craney, a spokesman for the Massachusetts Fiscal Alliance. “The Governor may be holding on to the wishful thinking that the migrant situation is under control, but it’s not.”

“Legislative leaders and our Governor refuse to reform the policies that make Massachusetts a migrant magnet and instead throw taxpayer money at the problem,” Craney added.

Craney’s statement came after a reporter for WCVB Channel 5 posted photos on X, formerly Twitter, of migrant families sleeping on the floor in Terminal E at Logan Airport early Thursday morning.

Gov. Maura Healey turned to the state-operated Melnea A. Cass Recreational Complex in Roxbury in late January to house migrant families that had been staying overnight at Logan, but the facility quickly neared its 400-person capacity a week after its opening.

The United Way has said a goal of the Fort Point shelter is to “prevent families from sleeping at Logan Airport, train stations, and other places not meant for human habitation.”

Only families who are documented are eligible for the state’s emergency assistance shelter system, according to the Executive Office of Housing and Livable Communities.

Families have been informed local hospitals and the airport are not shelters.

The Massachusetts Port Authority, which owns Logan, reported last November that roughly 20 to 25 migrants arriving daily had started to camp out in a baggage claim and elsewhere.

That number grew sharply, with 100 migrants sleeping overnight in Terminal E — the airport’s primary international terminal — in late January.

“We continue to see migrants at the airport,” Massport spokeswoman Jennifer Mehigan said in a statement. “They come to Logan a number of ways — some fly in, but the majority do not. They also arrive at Logan at all hours.”

Gov. Maura Healey on Thursday said she is open to reforming the state-run shelter system, to address capacity concerns such as imposing residency requirements or time limits.

The system has been maxed out at the 7,500 family limit for months.

The House is considering a supplemental budget that taps $873 million in surplus dollars from the pandemic to plug a $224 million shelter budget gap this fiscal year and pay down costs in the next, when spending is expected to approach $1 billion.

“It’s an incredibly frustrating situation,” Healey said. “I talked to other governors who are fed up with Congress, who are fed up with federal inaction.”