Officials say the test was aimed at verifying the capability to carry a "large scale heavy nuclear warhead".
Sunday's launch was of a "newly-developed mid/long-range strategic ballistic rocket, Hwasong-12", the official KCNA said, adding that leader Kim Jong-Un "personally oversaw the test-launch of the new type of rocket".
The U.S. military's Pacific Command said the weapon fired was "not consistent with an intercontinental ballistic missile", but according to missile expert John Schilling, the test "represents a level of performance never before seen from a North Korean missile".
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.
Last week the South also elected a new president, Moon Jae-In, who advocates reconciliation with Pyongyang and said at his inauguration that he was willing "in the right circumstances" to visit the North to ease tensions.
Nikki Haley, the USA ambassador to the United Nations, blasted North Korea's latest missile test Sunday, saying it "is not the way to sit down" with President Donald Trump. "The president said we are leaving open the possibility of dialogue with North Korea, but we should sternly deal with a provocation to prevent North Korea from miscalculating".
The missile fired was "not consistent with an intercontinental ballistic missile" according to the U.S. military's Pacific Command.
Ji also repeated an assertion by North Korean officials that Pyongyang has successfully foiled a CIA-backed plot to kill leader Kim Jong Un last month with a biochemical poison.
North Korea's missile test on Sunday was the country's most successful yet, according to analysts, who say Pyongyang may now have a weapon capable of hitting a key United States military base in the Pacific.
The White House, in a statement, said that North Korea has been "a flagrant menace for far too long".
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North Korea's latest ballistic missile test may be almost as big a deal as its propaganda machine claims.
North Korea said it fired the missile at a high angle to avoid neighboring countries. While Pyongyang frequently exaggerates its claims, the distances were roughly similar to those given by U.S., Japanese and South Korean military officials. While Pyongyang regularly tests shorter-range missiles, it is also working to master long-range missiles.
Nikki Haley, the USA ambassador to the United Nations, said Sunday that America and its worldwide partners will continue to "tighten the screws" on North Korea and leader Kim Jong Un.
U.S. Strategic Command said they were "presumed" to be Musudans, which are technically capable of flying as far as 2,400 miles, putting Guam within range and nearly reaching Alaska. "North Korea's missile launch is a serious threat to Japan and clearly violates. the United Nations resolution". "So if their ICBM has three stages, and this is a single-stage missile, maybe we're watching the North Koreans test the first stage of what will be a multiple stage ICBM".
South Korea's military said on Monday more analysis was needed to verify claims the missile test was a technical advancement.
The Security Council has adopted six increasingly tougher sanctions resolutions against North Korea.
In April it put dozens of missiles on show at a giant military parade through the capital, including one that appeared to be the type launched on Sunday.
The prime minister said it was another example of the rogue state's "reckless and provocative and unlawful conduct".
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.