Seoul and Washington agreed to deploy the Terminal High Altitude Area Defense (THAAD) system in the South after North Korea conducted a series of missile launches in the wake of its fourth nuclear test in January.
The decision was condemned by Pyongyang and also caused a damaging rift between Seoul and Beijing, which sees the deployment as a US bid to flex its military muscle in the region and undermine China's own missile capabilities.
Brooks also that that recent calls for South Korea to have its own nuclear arsenal to deter the North would seriously "complicate" the situation in the Asia-Pacific region, Yonhap news agency reported.
South Korea in September announced a new location for deploying THAAD, after vocal protests from local residents near the original site over potential health and environmental hazards.
Since Seoul and Washington announced the THAAD deployment was going ahead, North Korea has continued to conduct missile tests and carried out a fifth nuclear test on September 9.