The device was described as a “surface-to-surface medium-to-long-range ballistic missile”, according to the Korean state news agency KCNA, Joinfo.com reports with reference to the BBC.
South Korea’s defence ministry called it an armed provocation to test the response of US President Donald Trump.
North Korea’s latest ballistic missile test has been widely condemned.
The US, Japan and South Korea have requested an urgent meeting of the United Nations Security Council to discuss the incident.
KCNA reported that the test of the Pukguksong-2 missile, a new type of strategic weapon said to be capable of carrying a nuclear warhead, was overseen by leader Kim Jong-un.
It added that the missile was fired at a high angle in consideration of neighbouring countries.
The rocket used a solid-fuel engine, the report said, which gives ballistic rockets greater power and range.
South Korea military experts said the rocket had been launched by a “cold-eject” system, which uses compressed gas for its initial thrust, a system employed for submarine-launched missiles.
The report also said that Kim Jong-un “expressed great satisfaction” over the test launch, which it said “adds to the tremendous might of the country”.
South Korea and US officials said the missile flew east towards the Sea of Japan for about 500km (300 miles).
The missile reached an altitude of about 550km (350 miles), the South Korean military said.
Experts suggest the tests are programmed for shorter distances to avoid a missile landing on Japan.
This was the latest in a series of tests in the past year, including North Korea’s fifth of a nuclear device.
The launch took place at 07:55 local time (22:55 GMT Saturday) from the Panghyon air base in North Pyongan province on the west side of the Korean peninsula.
United Nations resolutions forbid North Korea from carrying out ballistic missile tests – part of wider efforts to prevent it becoming a fully nuclear-armed power.
South Korea’s foreign ministry said that “North Korea’s repeated provocations show the Kim Jong-un regime’s nature of irrationality, maniacally obsessed in its nuclear and missile development”.
Nato also condemned the missile test, with Secretary General Jens Stoltenberg urging North Korea “not to raise tensions further and to re-engage in a credible and meaningful dialogue with the international community”.
The European Union joined the criticism, declaring in a statement that North Korea’s “repeated disregard of its international obligations is provocative and unacceptable”.
Japan’s Prime Minister Shinzo Abe, standing next to Mr Trump on a visit to the United States, said the test was “absolutely intolerable”.
As for the US, Mr Trump said on Saturday: “America stands behind Japan, its great ally, 100%.”
China, North Korea’s closest ally, has yet to comment. Beijing has joined in international efforts to press Kim Jong-un to rein in his nuclear ambitions.