Han Min-koo told South Korea's parliament that Sunday's test had been detected by the controversial U.S. THAAD anti-missile system, which was deployed in South Korea last month, infuriating China.
Haley's comments came as the UN Security Council met to discuss how to respond to North Korea's latest ballistic missile test over the weekend.
Moon was elected to office on May 9 and reportedly plans to send diplomats to the United States, China, Japan and Russian Federation this month to discuss approaches to North Korea.
During his telephone conversation with the Japanese prime minister following his election and inauguration last week, the new South Korean president flatly laid out that most of his people could not accept or agree with the agreement signed by the former conservative Park Geun-hye administration.
"We are going to send a very strong, unified message to North Korea", she said.
"If you are supporting North Korea, you are against the rest of the global community", Haley said.
New South Korean President Moon Jae-in will visit the White House next month for a summit with President Donald Trump amid worries over North Korea's progress in building a nuclear and missile arsenal, Seoul's presidential office said Tuesday.
"Not one country is immune to the threat from North Korea", she added.
Haley: US Might Look at Sanctions on Countries Aiding North Korea
The council on Monday unanimously condemned North Korea's latest missile test and warned of new sanctions. Both are in defiance of United Nations sanctions.
North Korea seemingly rebuffed Moon's offer to talk by test-firing a missile on Sunday in violation of United Nations sanctions, saying the launch was a "newly developed ballistic rocket" capable of carrying a nuclear warhead.
"There was a basic exchange of opinions about North Korea's nuclear and missile provocations", Yoon said about the meeting between Chung and Pottinger.
President Moon Jae-in's special envoys began embarking on trips Wednesday to discuss possible summit talks between the new South Korean leader and his counterparts in the United States, Japan, China and Russian Federation.
Yoon said the sides have agreed to hold the summit in Washington in late June.
The countries also confirmed that Moon and Trump shared four broad principles in dealing with the North Korean nuclear crisis, Yoon said.
The U.S. ambassador the United Nations, Nikki Haley, said the United States believed it could persuade China to impose new U.N. sanctions on North Korea and warned that Washington would "call out" states supporting Pyongyang and target them with sanctions too. "Fourth, to achieve these goals, South Korea and the United States will pursue drastic and practical joint approaches".
North Korea says Sunday's launch tested the capability to carry a "large-size heavy nuclear warhead" and its ambassador in Beijing said on Monday that Pyongyang would continue such test launches "any time, any place".
While most of the attention in South Korea has been on the onerous challenges facing the country's new leader Moon Jae-in, many are paying more attention to the government's "handsome squad" of good-looking public officials that includes the president himself.
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