"He (Kim Jong Un) noted with pride that the results of the test-fire proved in actuality that the DPRK joined the front rank of the military powers fully equipped with nuclear attack capability," the Korean Central News Agency said Thursday.
Kim apparently gave field guidance for the test from a observatory post. After he gave the order, the submarine submerged to a firing depth and launched the missile North Korea calls "Pukguksong."
North Korea's launch took place in the waters, off Sinpo, South Hamgyong Province.
The US mainland and its "operational theater in the Pacific" are now within North Korea's "striking range," KCNA quoted Kim as saying.
He warned the US and South Korea to refrain from "hurting the dignity and security of North Korea" if it wants to avoid deadly strikes.
KCNA did not provide any details of where and when this test took place. It was not immediately clear whether this report was referring to the test that the South Korean Joint Chiefs of Staff confirmed on Wednesday.
Missile enters Japanese zone
The South Korean military said earlier that North Korea fired a missile that flew 500 kilometers before falling into the waters of Sea of Japan, also known as the East Sea.
The South Koreans did not comment on whether the test was successful.
This was the first time a North Korean missile entered Japan's air defense identification zone, Japanese Prime Minister Shinzo Abe said.
The launch comes amid the annual joint military exercise between the United States and South Korea, which kicked off on Monday.
The annual drill includes 25,000 US troops, the bulk of which are already stationed in Korea, according to a statement by US Forces Korea.
Compared to previous tests, Wednesday's missile is seen as "an improvement," according to the South Korean Joint Chiefs of Staff. The United States and South Korea are closely analyzing the details.
Dr. Daniel A. Pinkston, a professor at Troy University, told CNN the fact that the rocket traveled as far as it did suggests the North Koreans are "making quite rapid progress, and probably more rapid progress than any people had predicted."