The missile was launched on an unusually high trajectory, with KCNA saying it flew to an altitude of 2,111.5km and travelled 787km before coming down in the Sea of Japan.
Suggesting, say experts, that North Korea's missile range is growing - sparking condemnation of the launch and of the leader who ordered it.
The session had been requested by the United States and Japan on Sunday, shortly after North Korea's test launch of an intermediate-range ballistic missile.
North Korean ambassador to China Ji Jae-ryong also said Pyongyang's ballistic missile test was part of the country's efforts to develop ways to defend itself.
Under UN resolutions, North Korea is barred from developing nuclear and missile technology.
The North fired a ballistic missile that landed in the sea near Russian Federation on Sunday in a launch that Washington called a message to South Korea, days after its new president took office pledging to engage Pyongyang in dialogue.
Moon, South Korea's first liberal leader in almost a decade, said as he took his oath of office last week that he'd be willing to visit the North if the circumstances were right.More news: Appalachia's approach to drugs at odds with AG policy
"Let this latest provocation serve as a call for all nations to implement far stronger sanctions against North Korea", the White House said of the latest test. The launch is perceived to be a threat to South Korea, the US and even most nations around the globe.
Australia's prime minister has called on China to use its leverage over North Korea to end the regime's missile testing. Yet 38 North also says new assessments of what North Korea's missile program can do are now necessary.
Russian President Vladimir Putin said the test was risky, but warned against attempts to "intimidate" Pyongyang. Moon chaired an emergency meeting of security advisers early Sunday, within hours of the missile launch.
North Korea has claimed that the missile it tested on Sunday was a new type of rocket capable of carrying a large nuclear warhead.
Tensions have simmered on the Korean peninsula since April, when Kim and his government conducted a series of missile tests that demonstrated both the country's growing military capability and its willingness to remain belligerent in the face of global pressure.
Tensions between the United States and North Korea reached a peak in recent weeks, with Washington saying military action was an option under consideration and Pyongyang issuing threats of its own.
Kim also told scientists to "continuously develop more precise and diversified nukes and nuclear striking means" and "make preparations for more tests till the US and its vassal forces" use reason to make the "right choice", the KCNA reported.