Haley said the global community wants to be able to support North Korea, but as long as it continues trying to grow its nuclear program with missile tests, North Korea would remain an "island".
"We have to look into issues including the possibility of sending back THAAD, if it has not properly undergone domestic legal procedures", Woo said during a radio interview. South Korea has "been informed only of the fact that the North Korean missile was detected over the phone and through word of mouth".
U.S. Pacific Command Commander Adm. Harry Harris Jr. shakes hands with guests after deliverinfg a speech at the Sasakawa Peace Foundation, Wednesday, May 17, 2017, in Tokyo. "Kim Jong Un is not afraid to fail in public and every test he makes is a success because it takes North Korea one step closer to being able to deliver a nuclear-equipped missile anywhere in the world".
The day after the launch, North Korea claimed the fired missile, called Hwasong-12, reached an altitude of 2,111.5 kilometers, suggesting that it was a new type of intermediate-range ballistic missile.
Moon won the South Korean election last week campaigning on a more moderate approach towards the North.
"What about North Korea intimidating us?"
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South Korean Unification Ministry spokesman Lee Duk-haeng told reporters the government's most basic stance was that communication lines between North and South should reopen.
"If you are supporting North Korea, you are against the rest of the worldwide community", Haley said.
North Korea and the rich, democratic South are technically still at war because their 1950-53 conflict ended in a truce, not a peace treaty.
China has strongly opposed THAAD, saying it can spy into its territory, and South Korean companies have been hit in China by a nationalist backlash over the deployment.
North Korean officials accused the U.S. of pressuring other countries into severing or degrading diplomatic ties with it by misusing "sanction resolutions" against it.
North Korea has justified its latest long-, medium-range ballistic missile test-firing as "routine work to raise nuclear capability for self-defence", rejecting the UN Security Council's condemnation. Haley said, adding that Russian Federation had it "all wrong".