"This is being put together incrementally and of all the countries and all the issues you deal with، North Korea is not the one to be kludging together statements by the president and cabinet secretaries because the risk of miscalculation is so high،" Medeiros said by telephone from Tokyo، Japan.
Guam Governor Eddie Calvo dismissed the threat and said the island was prepared for "any eventuality" with strategically placed defences.
US Secretary of State Rex Tillerson sought to play down the rhetoric.
He was responding to reporters' questions on the North Korean nuclear capabilities. It is now far stronger and more powerful than ever before.
United States military officials played down the potential for military conflict.
The United States and South Korea remain technically still at war with North Korea after the 1950-53 Korean conflict ended with a truce, not a peace treaty.
North Korea has repeatedly denounced the THAAD deployment and escalated its threats after the United Nations Security Council voted 15-0 last week to impose tougher sanctions on the North.
The army will complete its plans in mid-August, ready for North Korean leader Kim Jong Un's order, KCNA said on Wednesday, citing General Kim Rak Gyom, commander of the Strategic Force of the Korean People's Army. He said his previous "fire and fury" warning to Pyongyang might have been too mild.
During his first official visit to DIU-x, Mattis will meet with staff and discuss with key leaders in the technology community how the Defense Department "can leverage new commercial technologies and methodologies and further expand initiatives created to accelerate fielding capabilities to the warfighter", Davis said.
"Americans should sleep well at night", Tillerson said as he flew from Malaysia to Washington, stopping in Guam to refuel.