Last month, U.S. Secretary of State Rex Tillerson directly called on the global community to act before North Korea carries out a more serious provocation and to impose new sanctions.
"No one is immune to the threat of North Korea", she told reporters before emergency closed-door consultations by the UN Security Council on the North's weekend ballistic missile launch, which experts said demonstrated a significant technological jump with the rocket flying higher and for a longer period of time.
U.S. President Donald Trump's administration has called for an immediate halt to North Korea's missile and nuclear tests, and U.S. Disarmament Ambassador Robert Wood said on Tuesday that China's leverage was key and Beijing could do more.
The test launch was a legitimate act of self-defence and U.S. criticism was a "wanton violation of the sovereignty and dignity of the DPRK [Democratic People's Republic of Korea]", a North Korean diplomat told the UN Conference on Disarmament in Geneva on Tuesday.
No draft resolution was circulated to the full council, but Haley said the United States was working with China on a text.
The envoy said at the outset of the meeting, which was open to the media, that the two countries "have in common a practical interest to deal with the North Korean nuclear issue".
"We want to look at the current sanctions in place and we want to look at strengthening the sanctions".
Now, the missile test-launch by Pyongyang can be interpreted as an outright rebuff to Moon's goodwill rhetoric, indicating that the Kim regime is not going to go easy on the new government in Seoul.
"It is considered an IRBM (intermediate range ballistic missile) of enhanced caliber", he said, referring to a class of missile created to travel up to 3,000 to 4,000 kilometers.
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China has strongly opposed THAAD, whose radar it fears could be used to spy in its territory, despite assurances from Washington that THAAD is purely defensive.
Pyongyang said the new weapon - called the Hwasong-12 - was capable of carrying a "heavy nuclear warhead".
The US vessel is reportedly still patrolling in the region.
On Monday, the U.N. Security Council said it was vital that North Korea show "sincere commitment to denuclearization through concrete action and stressed the importance of working to reduce tensions".
"The United States is not past looking at third-country entities who are helping North Korea, and putting sanctions on them, because if you are supporting North Korea, you are against the rest of the worldwide community".
North Korea's foreign ministry rejected the statement, saying it infringed on its right to self-defense, particularly as the missile was sacked at a sharp angle to ensure the safety of neighboring countries.
It is too premature, he said, to have any US-North Korea talks. "Clearly, there is a lot more leverage that China has, and we would like China to use", he said.
It comes as North Korea vows to continue secret underground nuclear explosions and ballistic missile tests as the sabre rattling hermit kingdom bolsters its military capability.
Earlier this month, naval exercises were conducted off the Korean Peninsula by the aircraft carrier USS Carl Vinson, with South Korean and Japanese aircraft also taking part.
Another carrier, the Ronald Reagan, left Yokosuka in Japan on Tuesday on its regular spring patrol, which would last three to four months, a spokesman for the U.S. Seventh Fleet said.