"We are deeply saddened by reports that two children adopted from Asia were among those killed in Washington state. We are seeking more information about the case," the unnamed official said.
The official stressed that no further comments would be provided out of respect to the privacy of those involved.
David Wayne Campbell, 51, was said to have shot and killed his wife, two children and an unidentified person before turning the gun on himself in Belfair, Mason County, on Friday.
The county coroner later identified three victims: Lana J. Carlson, 49; Quinn Carlson, 16; and Tory Carlson, 18.
A 12-year-old girl believed to be related to the victims was found at the site unhurt. The identity of a fourth victim has not been released until notification of next-of-kin.
Local media reports cited preliminary information alleging that the two teenagers may have been adopted in Russia. Later unconfirmed reports claimed the teenagers may have been born in Kazakhstan.