The State Department did provide one earlier denial (stating that the Iraqi Jewish archives were in the "temporary custody" of NARA and that "all the material will return to Iraq at the conclusion of the [conservation] project"). Otherwise, however, the U.S. has not been actively rebutting the steady flow of questionable allegations from the Iraqi Minister of Tourism, which has reportedly had the not insignificant consequence of Iraq suspending cooperation with U.S. archaeological teams (see here and here).
I asked public affairs at both NARA and the State Department for comment on these most recent allegations, but have not received a response from either.