After watching the launch of the Hwasong-15, the North's leader Kim Jong-Un "declared with pride that now we have finally realised the great historic cause of completing the state nuclear force", the official KCNA news agency said.
The test triggered global outrage with US Defense Secretary Jim Mattis saying it marked a significant step toward North Korea building missiles that can "threaten everywhere in the world, basically."
It was the first missile test of any kind since September 15, and squashed speculation that the North may have held back in order to open the door to a negotiated solution to a nuclear standoff.
"The ICBM Hwasong-15 type weaponry system is an intercontinental ballistic rocket tipped with super-large heavy warhead which is capable of striking the whole mainland of the US," KCNA said.
It said the development of the weapon would defend the North against the "US imperialists' nuclear blackmail policy and nuclear threat".
While Pyongyang has yet to prove its mastery of the re-entry technology required to bring a warhead back through the Earth's atmosphere, experts believe it is on the threshold of developing a working intercontinental nuclear strike capability.
Wednesday's test caused deep consternation among the North's neighbours.
Japanese Prime Minister Shinzo Abe called it an intolerable, "violent" act and South Korean President Moon Jae-In condemned Pyongyang's "reckless" behaviour.
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