Officials in three Northern Virginia counties are scrutinizing the costs of educating the nearly 2,000 unaccompanied immigrant children living there with an eye toward recouping expenses from the federal government for keeping the young migrants — who crossed the U.S. border without their parents — in local public schools.

The children, most of whom entered the country in a wave of unaccompanied minors from Central America, have been released to sponsors in various jurisdictions. The federal Office of Refugee Resettlement says there are 1,775 such children in the three counties: 1,131 in Fairfax, 417 in Prince William and 227 in Loudoun.

The issue is filled with political tension, as the Obama administration has sought refuge for the immigrant children amid a long-standing debate about how best to secure the U.S. border and how to treat those who cross illegally. There has been special attention to children who enter the country unsupervised as there was an increase this year that has just begun to ebb.

With some of those children landing locally, the boards of supervisors in Fairfax and Loudoun have in recent weeks approved studying the cost of educating the minors. U.S. public school systems generally have a mandate to educate all children in their district regardless of their legal status.

Prince William Supervisor Peter Candland (R-Gainesville) posted an online petition this week asking the federal government to pay the per-pupil cost of educating refu­gee children who have enrolled in the county’s schools.

“We’re obligated by law to provide them an education, and I absolutely believe that that is what we need to do,” Candland said. “We don’t have the money. It’s the taxpayers that already live here that are suffering from these children moving here. We need help from the federal government. We need help if they’re going to send the kids to these localities.”

Candland launched his petition independently and said he does not know whether other county supervisors will support it. Prince William has at times been in the immigration spotlight because of county policies that aggressively enforced anti-illegal-immigration efforts.

Corey Stewart (R), chairman of the Prince William Board of County Supervisors, said he would be willing to sign Candland’s petition but does not expect it to be effective.

“The good that it will do is just to emphasize that there is a cost to local taxpayers of the federal government’s failure to control the border,” he said. “We shouldn’t expect a check in the mail from the federal government.”

Prince William school board member Alyson Satterwhite (Gainesville) said she is concerned about the cost, calling it a “significant amount of money” if all the students enroll in county schools.

“If the federal government is putting the burden on us and not providing the funds to pay for it, that’s an issue to talk about,” she said.

In September, Fairfax Supervisor Pat Herrity (R-Springfield) asked the county to review the cost of hosting the migrants, including how much taxpayers will spend on education and other services for the children. Herrity said the county executive’s office is due to complete a report by the end of this month.

He said he expects to request funding from the federal government after he knows the costs.

“We’ll look at what avenue or avenues there are for us and hopefully make a decision to seek reimbursement,” he said. “It really is a federal responsibility, and Fairfax County’s being hit pretty heavily.”

Loudoun also is studying the effects of the young migrants’ arrival here and the possibility of asking for federal money after a motion by Supervisor Eugene A. Delgaudio (R-Sterling) passed last week.

Federal laws do not permit schools to require new students to disclose their immigration status, so county officials are unable to tally the precise cost of educating newly arrived immigrants.

Herrity said that Fairfax schools would spend more than $14 million to educate the 1,131 refugees over the course of a full school year if they all enrolled, based on a per-pupil cost of $14,755 for each English language-learner in the county’s schools.

Candland said in his petition that Prince William would spend more than $12 million during the school year, an amount based on a student population of more than twice as many unaccompanied children as are now living in Prince William. His calculation accounted for children continuing to arrive in Prince William at the same monthly rate, even though the rate of children crossing the border has dropped since the summer.

Prince William schools spokesman Phil Kavits said preliminary numbers this year do not show a spike in students needing extra English-language education. Although the district continues to grow by about 2,000 students a year, the proportion of those requiring extra help with learning English has fallen slightly.

“Contrary to the idea that we’re seeing a major spike in any kind of student, that’s not what we’re seeing thus far this year,” Kavits said.

A Loudoun schools spokesman said that migrants make up “a very small percentage” of new students in the school system and that the school district has had no problems accommodating them.

Eric Williams, Loudoun’s new schools superintendent, said the district is accustomed to handling students who have recently arrived from other countries.

“It’s not necessarily so atypical, because we’re used to welcoming and integrating into our school communities immigrants, whether they be documented or whether they be refugees,” he said. “We don’t get into the politics. . . . Students appear in the community, and we’re committed to serving them.”