State-run KCNA news agency confirmed on Tuesday that North Korean leader Kim Jong Un guided a drill simulating a "nuclear counterattack," the latest in a volley of tests by Pyongyang this year.
Seoul's military had earlier claimed that the North had fired several short-range ballistic missiles on Monday, with Tokyo confirming the launch.
According to the report, Kim guided a combined tactical drill simulating a nuclear counterattack involving super-large multiple rocket artillerymen.
The rockets "hit their island target" about 352 kilometers (219 miles) away, and Kim was described as "expressing great satisfaction."
On Monday, South Korea's military reported that missiles launched from the Pyongyang region traveled over 300 kilometers before exploding in the waters to the east of the Korean peninsula.
It called the launch a "blatant provocation."
A government spokesman in Tokyo has also confirmed the launch, saying that one missile reached a maximum height of 50 kilometers and landed outside the country's EEZ.
Pyongyang conducted its second launch in less than a week on Friday, testing a "super-large warhead" intended for a strategic cruise missile. Military personnel in Seoul at the time confirmed that it had seen cruise missile launches.
The launch follows Moscow, an ally of Pyongyang, effectively ending UN monitoring of sanctions violations against Kim's government for its nuclear and weapons development in March by using its veto power in the UN Security Council.
Analysts said that North Korea may be testing cruise missiles before transferring them to Russia for use in Ukraine. Washington and Seoul think Kim has already sent weapons to Moscow, even though UN sanctions ban such actions.
It has also increased testing, saying it tested a new solid-fuel, medium-to-long-range hypersonic missile in early April.