The Loudoun County Board of Supervisors will seek federal reimbursement for costs associated with more than 200 undocumented immigrant children who have been relocated to the county after crossing the U.S.-Mexico border.

The board voted Wednesday to authorize a letter to President Obama and the county’s congressional and state delegations to express concern about the “unfunded federal mandate” resulting from the resettled children. The letter will also request that the federal government foot the bill for any resulting, local-tax-funded costs within the county school system or other public services.

This month, the board asked county staff members to investigate the potential financial and health effects of the reported 227 unaccompanied minors who have been placed with sponsors in Loudoun. At Wednesday’s meeting, Assistant County Administrator John Sandy reported that 28 children within the school system have been identified as unaccompanied minors and that the estimated cost of their education for the current fiscal year is about $225,000.

County staff members said those 28 students have been distributed across Loudoun’s primary and secondary schools. School officials said that the addition of students is neither unusual nor creating any hardship in the system.

Under federal privacy law, the immigration status of a newly arriving student can be voluntarily disclosed but is not requested by the school system. Loudoun has registered a total of 87 students identified as refugees between July 1 and Sept. 30. Twenty-eight of these are unaccompanied — meaning they were sent to live with a relative or friend who does not have custody of the child, according to the staff report.

Several supervisors expressed frustration Wednesday that the county could account for only 28 of the 227 unaccompanied children reported by the U.S. Office of Refugee Resettlement.

“Where are the missing children?” asked Supervisor Eugene A. Delgaudio (R-Sterling), who proposed the original motion to request more information about the resettled minors. “We can’t declaratively say what the costs are to us unless we know where they are. . . . What do I tell my constituents?”

Because of regulations aimed at protecting the privacy and safety of the refugee children, information about their whereabouts is not publicly available. Supervisor Kenneth D. Reid (R-Leesburg) said it was unfortunate that the government could not do more to thoroughly assess the potential financial impact for county taxpayers.

“I know there are some people out there, our political opponents think that we are on a witch hunt,” Reid said. “We are not. We are looking out for the taxpayers of Loudoun County, that’s what we’re concerned about.”

Several supervisors said they were troubled by the possibility of illnesses spread by the undocumented children.

School and county officials said that no evidence has been presented by either the Centers for Disease Control and Prevention or the county health department to indicate that the students from other countries represent any public health concern. But board Chairman Scott K. York (R) said he was less than impressed with the federal government’s abilities concerning potential health threats.

“We’re dealing with issues around this world right now, and I think the government, the federal government, is clueless, and putting the public at risk,” York said. “I just want to make sure that we are fulfilling our role and that we are protecting all the citizens of Loudoun County.”

Children who arrive in Loudoun through the Refugee Resettlement Office have received required immunizations, school officials said. But some supervisors remained concerned.

“It’s great that the 28 children have all gotten their immunizations, but as we’ve learned very recently with Ebola, you don’t have to be in school to become ill,” Supervisor Suzanne M. Volpe (R-Algonkian) said.

The board’s worries about possible health threats posed by undocumented minors — particularly linked to discussions about the Ebola virus — have drawn criticism from the Loudoun County Democratic Committee, which previously accused supervisors of “stoking unwarranted fears.”

Supervisor Shawn M. Williams (R-Broad Run), who abstained from the board’s Oct. 1 vote to investigate the fiscal impact of the unaccompanied minors, was the lone supervisor to voice concern Wednesday about the motivation behind the board’s inquiry.

“I still have concern . . . that this is not really about the cost impacts to the county but more about partisanship,” Williams said. “I do not want to uproot, invade the privacy [of], make . . . uncomfortable, this small amount of children that our community is supporting.”

The county staff report said the local health department and the county’s department of family services have not noticed any “marked increase” in the demand for their services as a result of the unaccompanied minors.

The fiscal impact for government services is “minimal at best, even though the Health department is unable to ask for documentation by federal law,” the report said.

The board unanimously voted to have county staff members write a letter to state and federal authorities. The letter will be from York on behalf of the board.

Supervisor Ralph M. Buona ­(R-Ashburn) was absent for the vote.