In a broadcast on state TV, North Korea said the newly developed Hwasong-15 has "much greater advantages in its tactical and technological specifications and technical characteristics" than its Hwasong-14 ICBM, tested twice in July.
Analysts and officials are awaiting the release of photos and video from the launch to identify what differences there may be between the Hwasong-15 and previous North Korean missiles.
The missile, the first test in 75 days, was fired on a steep trajectory and flew for 53 minutes, North Korea said. It reached an altitude of 4,475 km (2,780 miles) and flew 950 km (590 miles), according to the North.
"If (today's) numbers are correct, then if flown on a standard trajectory rather than this lofted trajectory, this missile would have a range of more than 13,000 km (8,100 miles)," the U.S.-based Union of Concerned Scientists said in a statement.
That would suggest that all of the continental United States including Washington D.C. and New York could be theoretically within range of a North Korean missile.
On July 4, North Korea launched its first ICBM, Hwasong-14, which reached an altitude of 2,802 km (1,741 miles) and a range of 933 km (580 miles) during a flight of 39 minutes, North Korea's state media reported.
A second test of the Hwasong-14 on July 28 exhibited improved performance, with the missile flying for about 47 minutes to an altitude of 3,724 km (2,313 miles) and a range of 998 km (620 miles), according to state media.
The second flight showed the missile has a range of more than 10,000 km (6,213 miles), potentially putting the U.S. West Coast within range, analysts have said.
After Wednesday's test, Kim declared that with the Hwasong-15 North Korea had "finally realized the great historic cause of completing the state nuclear force."
International observers, however, said it remains unclear how heavy a payload the missile was carrying, and if it could carry a large nuclear warhead far enough to strike the United States.
North Korea launched the missile from Pyongsong, South Pyongan Province, about 30 km (18 miles) north of its capital, Pyongyang, the first time a missile was fired from this location.
Unlike many other tests that historically occur in the early mornings, Wednesday's launch occurred in the middle of the night in Korea, at around 2:28 a.m. North Korea's local time (6:17 p.m. GMT).
The location and timing are likely a reflection of Pyongyang's continuing efforts to test weapons from anywhere and at any time, providing more realistic tests and making it more difficult for other countries to predict and possibly intercept a launch.
"The test is unusual in that it was conducted in the dead of night, perhaps reflecting North Korean concerns about avoiding a U.S. ballistic missile defence intercept," the U.S.-based Centre for Strategic and International Studies said.
The previous two ICBM tests in July were launched from Panghyon airfield in North Pyongan Province, and in Mupyong-ni, Chagang Province, respectively.
Other, shorter range missiles have been launched from a variety of locations as well, including at least two intermediate-range ballistic missiles that flew over Japanese airspace in August and September.
The last of those missiles was launched at Sunan, just north of Pyongyang, from a "transporter erector launcher," a road-mobile vehicle that can make it more difficult to track and target missiles before they are launched.
(Reporting by Josh Smith in Seoul, Editing by Soyoung Kim and Michael Perry)
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