The country's leader, Kim Jong Un, supervised the launch of the Hwasong-12 missile that reached an altitude of 2,111.5 kilometers (1,312 miles) and flew 787 kilometers (489 miles), KCNA said.
The test was "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.
North Korea warned the United States not to provoke it, saying the "US mainland and Pacific operations" are within range of North Korean missiles, KCNA said.
US officials said the missile launched near the city of Kusong, in western North Korea, flew across the country and into the Sea of Japan/East Sea, hitting the water about 60 miles from Vladivostok in eastern Russia.
Russia, however, said the missile fell 310 miles (500 kilometers) from its coast, according to a report on RT.com.
Japan's Defense Ministry said the missile reached an altitude of 2,000 kilometers (1,240 miles) and flew for 30 minutes.
The high altitude and longer flight time indicate a missile with an extended range, according to David Wright, co-director of the Union of Concerned Scientists.
Writing on his organization's blog, Wright pointed out that if the missile did reach that height and fly that long, it could reach the US territory of Guam in the Pacific.
Guam is home to Andersen Air Force Base, through which the US Air Force rotates heavy bombers including B-1s, B-2s and B-52s.