The National Archives and Records Administration (NARA), which implements the executive branch-wide CUI Program and oversees federal agency actions to comply with Executive Order 13556. NARA has delegated this authority to the Director of the Information Security Oversight Office (ISOO).
Sources:
NIST SP 800-171r3
from
32 C.F.R., Sec. 2002
NIST SP 800-172
from
32 C.F.R., Sec. 2002
NIST SP 800-172A
from
32 C.F.R., Sec. 2002