The drill took place on Monday, according to the report. Seoul's military had earlier announced that the North had fired several short-range ballistic missiles on Monday, with Tokyo confirming the launch.

Kim "guided a combined tactical drill simulating a nuclear counterattack involving super-large multiple rocket artillerymen," the report said.

The rockets "hit their island target" some 352 kilometres (219 miles) away, it continued, describing Kim as "expressing great satisfaction."

South Korea's military said Monday that missiles flew from the Pyongyang area for about 300 kilometres before splashing down in the waters east of the Korean peninsula.

It branded the launch a "blatant provocation."

Tokyo also confirmed the launch, with a government spokesman saying one missile had a maximum altitude of 50 kilometres and landed outside of the country's EEZ.

The launch is the second in less than a week by Pyongyang, which on Friday tested a "super-large warhead" designed for a strategic cruise missile, state media said. Seoul's military confirmed it had detected cruise missile launches at the time.

The launch comes after Pyongyang's ally Moscow in March used its United Nations Security Council veto to effectively end UN monitoring of sanctions violations on Kim's government for its nuclear and weapons programme.

Analysts have warned that North Korea could be testing cruise missiles ahead of sending them to Russia for use in Ukraine, with Washington and Seoul claiming Kim has already shipped weapons to Moscow, despite UN sanctions banning any such moves.

Seoul claims Pyongyang has sent around 7,000 containers of weapons to Moscow for use in Ukraine.

The largely isolated country has recently bolstered military ties with Moscow, and this month it thanked Russia for its UN veto.

It has also ramped up testing, claiming in early April to have tested a new medium-to-long-range solid-fuel hypersonic missile.

Pyongyang's recent track record on launches indicates the North is trying to push its technical abilities, said Hong Min, a senior analyst at the Korea Institute for National Unification.

Monday's launch "appears to be a part of its weapons development programme that needs testing rather than ones that are fully developed," he told AFP.

Last year, the North conducted a record number of missile tests in defiance of UN sanctions in place since 2006 and despite warnings from Washington and Seoul.

Pyongyang declared itself an "irreversible" nuclear weapons state in 2022.