BOSTON (SHNS) – Massachusetts communities will “need to be ahead of the curve” to absorb an influx of asylum-seekers and other migrants expected to continue in the coming months, Boston Mayor Michelle Wu said Monday.

Boston has welcomed hundreds of new arrivals recently, Wu said, adding that many advocates warn the steady flow of migrants will continue for the next few months. She praised the state’s response as “great and amazing,” describing a “real acceleration” in standing up housing.

“Over the summer, our hospitals were absorbing much of the intake and community organizations were absorbing much of the intake, connecting people to various shelter options or housing,” Wu told WBUR’s Radio Boston. “When those frontline organizations reached capacity, then I think we saw the state really step into leadership on this.”

Gov. Charlie Baker has been pressing for more help from the federal government to support arriving migrants, and he filed a $139 million spending bill on Nov. 18 that would fund more than 1,300 temporary shelter units and cover the costs of shelter provider rate increases, a temporary central intake center, and placing new students in local schools.

“The influx of new arrivals and additional families seeking emergency assistance is a humanitarian crisis we must address across the Commonwealth,” Baker wrote in a letter to lawmakers alongside the bill.

Top Democrats on Beacon Hill have not mirrored Baker’s urgency, sending the legislation to the House Ways and Means Committee for review one week ago and otherwise offering no indication of how or when they plan to act.

“I worry that the flow will continue for the next few months — it’s what all the advocates are telling us, that we will need to be ahead of the curve in being able to absorb this capacity,” Wu said. “What we see in terms of the speed of action for our immigrant families is exactly what it should be, and we need to do even more. There are many other communities also that need to see that same speed of action.”

The Massachusetts Emergency Management Agency, or MEMA, in early December will begin using the Bob Eisengrein Community Center in Devens as an intake center where as many as 60 families or 125 individuals can reside during their first few days in emergency shelter. Officials plan to offer case management and other services at that location before transferring individuals to another emergency site or longer-term housing.

In just a bit more than five weeks, the administration’s response to migrant arrivals will become the responsibility of Gov.-elect Maura Healey.

Wu said Monday she still has not held an in-depth meeting with Healey since the Democrat cruised to victory nearly three weeks ago, though they have exchanged “a lot of messages back and forth” and appeared together at a handful of events.

“She needs time to get her transition up and running, to enjoy her Thanksgiving, so I’m ready and eager when we will get the chance to sit down,” Wu said. “We were aiming for this week, so we’ll see — I think there’s a lot happening this week across the city, but sometime in the next couple of weeks, I’m sure that will happen.”

Healey, who continues to serve as attorney general until she takes the oath of office as governor, and Lt. Gov.-elect Kim Driscoll met with Baker and Lt. Gov. Karyn Polito one day after the election.