President Moon ordered officials to consult with the USA on the temporary deployment of the four additional THAAD launchers, following the North's launch of a Hwasong-14 intercontinental ballistic missile on July 28th.
CHINA has demanded an immediate stop to deployment of the Terminal High Altitude Area Defense (THAAD) system in South Korea.
Trump is to speak Wednesday with China's president.
The ministry stressed the urgent need to mobilize the launchers amid growing threats from North Korea, which had its sixth and most powerful nuclear test on Sunday.
Two THAAD batteries have already been installed.
The United States and South Korea are moving forward with plans to install four more Terminal High Altitude Area Defense (THAAD) rocket launchers at a US base in Seongju, in spite of widespread opposition and protests from local residents and activists.
An additional four missile interceptors will be deployed on Thursday at a US military camp in South Korea, Seoul announced on Wednesday.
"Myself and President Putin share a view that North Korea has gone the wrong way with its nuclear and missile programme and that easing tension on the Korean peninsula is an urgent issue", Mr Moon said. He said it "offers a genuine way to defuse the tensions and a step-by-step settlement".
Russian Federation and China have proposed a "double-freeze" plan which would see Pyongyang suspend its nuclear and ballistic missile tests in exchange for a halt in joint US-South Korea military drills.