Last August, Pyongyang also successfully test-fired a submarine-launched ballistic missile (SLBM) 500 kilometers (300 miles) towards Japan, far exceeding any previous sub-launched tests, in what Kim hailed as the "greatest success".
Tensions are rising in the region as President Donald Trump seeks to prevent North Korea from acquiring the capability to strike targets in the continental USA with a nuclear weapon.
"This is a rogue regime that is now a nuclear-capable regime", McMaster said. Wu did not speak to the media after the talks.
Speculation of an imminent nuclear test is brewing as the North marks anniversaries including the 105th birthday of its founding leader on Saturday - sometimes celebrated with a demonstration of military might.
Trump also sent a message to North Korea and its ally China during his meeting with the Chinese president that he was willing to take action over Kim's nuclear program, said Lee Ho-ryung, chief of North Korean studies at the Korea Institute for Defence Analyses.
Taipei's response came after Trump met Xi at the USA president's Mar-a-Lago retreat in Florida from Thursday to Friday, in the first meeting between the two leaders.
But Tillerson did note Washington is prepared to come up with its own ways to solve the North Korea issue if Beijing doesn't work with the U.S.
"The two sides agreed to undertake an ambitious agenda and meeting schedule to show progress and demonstrate meaningful results", he said.
Seoul and Washington are also conducting joint military drills, an annual exercise which is seen by the North as a practice for war.
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Tillerson said Trump and the Chinese president "had extensive discussions around the unsafe situation in North Korea". South Korean and US forces are also involved in annual joint military drills that run until the end of April.
Even before the missile test, North Korea's nuclear program was expected to be an important talking point between Xi and Trump.
However, Pyongyang's response suggested the reclusive state was determined to continue with its nuclear weapons programme. So in the end, the U.S. must work with China to rein in North Korea. The North quit the negotiations in 2009.
The isolated North is barred under United Nations resolutions from any use of ballistic missile technology.
The U.S. military carried out a missile attack on Syria during Trump's meeting with Xi. But that summit took a backseat to the top-secret briefing by U.S. National Security Adviser H.R. McMaster, and Secretary of Defense Jim Mattis, an official familiar with the briefing told Reuters.
According to The Times, Xinhua published the editorial immediately after Xi had left the US following his weekend sit-down with Trump at the President's Mar-a-Lago estate in southern Florida.
In Tokyo, the feasibility of USA military action was downplayed, while South Korea said the focus remained on deterrence and readiness. But unlike Syria, experts warn that North Korea has a means of striking back if provoked.
Meanwhile, the USA, which has military forces in South Korea, is further stoking tensions with the North and China by deploying a navy strike group in the western Pacific Ocean near the Korean Peninsula.
"They agreed to increase cooperation and work with the global community to convince the DPRK to peacefully resolve the issue and abandon its illicit weapons programs", he said.