Haley said a plan is still in the works between the US, Japan, South Korea and China - North Korea's only major ostensible ally - to halt North Korea's progress on nuclear weapons and ballistic missiles.
Moon, who was sworn in last week, warned that the North's nuclear and rocket programmes were "advancing rapidly", days after Pyongyang launched what appeared to be its longest-range missile yet.
While FireEye researcher John Miller, too, said USA and European security officials maintain it was too early to say who is behind the attack, they did not rule out North Korea as a suspect.
The top United States military officer in the Pacific has said that North Korea's recent military actions are "a recipe for a disaster" and warned against a sense of complacency in the face of increasing tensions on the Korean Peninsula.
Separately, Mr Moon's envoy to the U.S. is travelling to Washington for talks about North Korea with United States president Donald Trump. "He said, however, that what he's willing to do is not talk for talk's sake but for talks that produce an outcome", the envoy said.
Although the two countries are allies, they are divided over the issue of whether South Korea has to pay for the Terminal High Altitude Area Defence (Thaad) anti-missile system deployed in the south of the country.
North Korea launched Sunday what appeared to be its longest-range ballistic missile yet, saying it was capable of carrying a "heavy nuclear warhead" in a test aimed at bringing the USA mainland within reach.
South Korea has complained that some of is companies doing business in China have faced discrimination in retaliation for the system's deployment.
But a senior North Korean diplomat has said Pyongyang is also open to having talks with Washington under the right conditions.
The Thaad deployment has already had an impact, after its TPY-2 radar component detected Sunday's missile launch.
Speaking to Lee, Chinese Foreign Minister Wang Yi said there had been some "undeserved setbacks" in relations this year, in apparent reference to THAAD. (Chinese) "We hope the new government of South Korea realizes the problems that both countries are facing and takes effective measures to remove such obstacles to put the development of bilateral relations back on track".
Later in the song, they refer to South Korea, saying, "this time, kid, you're going too far" and "your big brother's annoyed", a nod to China's view of itself as the pre-eminent political and economic power in northeast Asia.