The KCNA news agency quoted the country's Missile Administration as stating the test-fire, held on Wednesday, went as planned. It added that ruler Kim Jong Un oversaw the launch, DPA reported.
"The new-type tactical ballistic missile was tipped with a 4.5 tonnage super-large conventional warhead," KCNA reported.
The test aimed to check the "accuracy of hit at medium range of 320 km and explosive power of the super-large warhead with a missile loaded with such a warhead," the agency continued.
The same type of missile had been tested in July, according to Pyongyang.
On Wednesday, South Korea's military said the North had fired multiple short-range ballistic missiles.
The missiles, fired from north of Pyongyang, flew about 400 kilometers, South Korean news agency Yonhap cited the general staff in Seoul (JCS) as saying.
North Korea is prohibited by UN resolutions from launching or even testing ballistic missiles of any range.
These are usually surface-to-surface missiles that can also be equipped with a nuclear warhead.
Tensions have risen on the Korean Peninsula after Pyongyang significantly expanded its missile tests over the past two years, while sharpening its rhetoric against the US and South Korea. It has also strengthened its military cooperation with Russia.