The Korean Central News Agency said that Wednesday's test was of "great significance" and involved a Pukguksong-3 missile.
KCNA Watch has registered the lowest levels on its Threat Index since North Korean supreme leader Kim Jong Un came to power in 2011.
Russia's Sergei Lavrov has accepted the invitation of North Korea's foreign minister.
The state-controlled news agency commentary is the first official acknowledgement of a thawing in relations with the U.S.
In its latest commentary, North Korea's official news agency warned that "the right to preemptive attack is not exclusive to the U.S."
North Korea's state-run media said President Donald Trump "absolutely" needed medication to avoid starting a nuclear war.
Pyongyang's official news agency also likened South Korea's defense minister to Trump's dog.
As President Donald Trump tries to get South Korean President Moon Jae-in on board, North Korea warns nuclear war is closer than ever.