"The test-fire aimed at verifying the tactical and technological specifications of the newly developed ballistic rocket capable of carrying a large-size heavy nuclear warhead", KCNA said.
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.
Prime Minister Shinzo Abe told reporters Sunday that the launch, which is banned by the United Nations, is "absolutely unacceptable" and that Japan will respond resolutely.
U.S. President Donald Trump warned in an interview with Reuters this month that a "major, major conflict" with North Korea was possible. Each new nuclear and longer-range missile test is part of the North's attempt to build a nuclear-tipped intercontinental ballistic missile.
Abe also mentioned his willingness to hold an early summit between Japan, China and South Korea, in addition to his separate meetings with Xi and Moon.
Sometime over the weekend, North Korea finally managed to launch a missile that didn't immediately explode.
The country has conducted multiple successful nuclear tests since 2005 despite crippling worldwide sanctions and a concerted USA cyber campaign to disrupt their operations.
Kim Jong Un's regime fired yet another ballistic missile on a very steep trajectory - perhaps demonstrating a capability to conduct an electromagnetic pulse attack that could devastate the South with a single nuclear detonation outside the atmosphere.
China is the linchpin of Trump's strategy for halting North Korea's pursuit of a nuclear-tipped missile that could strike the US mainland.
Yoon quoted Moon as saying South Korea is "leaving open the possibility of dialogue with North Korea, but we should sternly deal with a provocation to prevent North Korea from miscalculating".
U.S. Ambassador to the United Nations Nikki Haley called the launch a message by Pyongyang to South Korea after the election of President Moon Jae-in, who took office on Wednesday.
The report on the missile's flight was largely consistent with South Korean and Japanese assessments on Sunday that it flew 700 km (435 miles) and reached an altitude of more than 2,000 km (1,243 miles), which is further and higher than an intermediate-range missile tested in February from the same region, northwest of Pyongyang. The mobile launcher allows the missile to be hidden until minutes before launch, and the solid-fuel engine allows it to be ready to launch immediately at any time.
Russian President Vladimir Putin said in Beijing that Moscow was opposed to any new countries acquiring nuclear weapons, but that the world should talk to North Korea rather than threaten it.
The White House says North Korea has been "a flagrant menace for far too long". He says Japan and the USA also started discussing the sanctions on North Korea, but did not elaborate. Reaching the US West Coast would require a missile with a range of more than 8,000 km. The USS Carl Vinson, an aircraft supercarrier, is also engaging with South Korean navy ships in waters off the Korean Peninsula, according to Seoul's Defense Ministry.