The propaganda from Pyongyang must be considered with wariness, experts have said, but the claim, if true, would bring the country a step closer to its goal of a nuclear-tipped missile able to reach the US mainland.
The missile flew for about 30 minutes, travelling about 800km (500m) before landing in the Sea of Japan, according to Tokyo.
North Korea’s official Korean Central News Agency described the missile as a “new ground-to-ground medium long-range strategic ballistic rocket”.
They added that the “Hwasong-12” was “capable of carrying a large, heavy nuclear warhead”.
North Korean leader Kim Jong Un had hugged rocket research officials after witnessing the test, saying they “worked hard to achieve a great thing”, they said.
US president Donald Trump has called for “far stronger sanctions” on North Korea after the country test-fired a ballistic missile.
In a statement, the White House said Pyongyang has been “a flagrant menace for far too long”.
“Let this latest provocation serve as a call for all nations to implement far stronger sanctions against North Korea,” it said.
Mr Trump “cannot imagine Russia is pleased” with the test as the missile landed closer to Russia than to Japan, the statement added.
Earlier, the US Pacific Command said it detected the launch and tracked the missile, but added that it “did not pose a threat to North America”.
“The type of missile is being assessed and the flight was not consistent with an intercontinental ballistic missile,” a spokesperson said.
The launch early on Sunday took place at a region, named Kusong, where the North previously test-launched an intermediate-range missile it is believed to be developing.
Tensions are running high in the Korean peninsula, with Mr Trump warning last month that a “major, major conflict” with Pyongyang was possible.
However, the US president has also said he is open to talks with North Korean leader Kim Jong Un over Pyongyang’s nuclear and missile programmes.
The launch is also the first since a new liberal president took office in South Korea on Wednesday.
Moon Jae-in has said dialogue and pressure must be used to ease tensions on the Korean peninsula and stop the North’s weapons pursuit.
The test drew an immediate response from Seoul and Tokyo, with the two leaders also talking over the phone to discuss a response.
In Seoul, presidential secretary Yoon Young-chan said Mr Moon “expressed deep regret over the fact that this reckless provocation… occurred just days after a new government was launched in South Korea”.
“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,” he added.
In Tokyo, Prime Minister Shinzo Abe said: “North Korea’s repeated missile launches are a grave threat to our country and a clear violation of UN resolutions.”
It was not clear what type of ballistic missile was fired.
While North Korea regularly tests shorter-range missiles, it is also working to master the technology needed to field nuclear-tipped missiles that can reach the US mainland.
The launch is the first in two weeks. The previous one ended in failure just minutes into flight.