Some of the state’s poorest school districts — already overwhelmed by immigrant children — are bracing for a new wave of Central American kids enrolling this fall that officials fear will further drain limited resources for English-speaking students.

“We certainly don’t want to communicate that our city is not a welcoming place, especially for young children, but we have to be concerned about our finances and our ability to serve all of our citizens,” said New Bedford Mayor Jon Mitchell. “If the point comes where we feel as though our resources are getting too strained, we’re going to look to the state and federal government for assistance because that is only fair.”

Mitchell said school officials told him four families — three from Guatemala and one from Honduras — recently released from immigration detention centers in Texas will be enrolling their kids in New Bedford public schools this fall.

The flood of immigrant students comes as the nation scrambles to absorb about 57,000 unaccompanied immigrant children who have swarmed across the country’s southern border since the fall. Gov. Deval Patrick said this week he wants to shelter some of those kids in Massachusetts after receiving a request from the Obama administration — a plan some say could tax local school budgets.

“We’re very concerned about an influx because our ability to support these students and their families will be compromised simply because we won’t be able to anticipate their needs,” said Elizabeth Barry, Brockton’s deputy superintendent of learning and teaching, who said the city has been hit already with an increase in students from Central America.

In Chelsea, City Manager Jay Ash said last year his school system was swamped by 267 students from Guatemala, El Salvador and Honduras, all of whom were not previously enrolled in a U.S. school — which represents a 65 percent increase from the year before and a 600 percent increase over four years.

“This is a stress on the entire system, and it is a stress that we need to have a conversation with our state and federal partners about resolving,” Ash said.

“Many of the kids that are coming, the unaccompanied minors that we’re talking about, are coming here with social and emotional issues that are disruptive in a classroom environment, so there’s a need for additional counselors.”

Quincy school officials are also adapting to suit the needs of the thousands of students coming from families whose first language isn’t English.

In 2005, 22 percent of the students in Quincy came from such families; by 2013, the number soared to 35 percent, representing 9,320 students district-wide, officials told the Herald.

In Everett, Mayor Carlo DeMaria said a wave of immigrant students would present a financial dilemma because “many of these students enter our system with unique issues that we have to address, all of which costs additional money.”

He added: “As a gateway community, many Everett children already struggle due to poverty, the increased burden on the schools prevents us from increasing programming for some other students, which is a continuing problem”