He said his government will "do its utmost" to protect the lives and assets of Japanese people.
Some experts have said that projectiles fired from the "super-large" multiple rocket launcher are virtually missiles or missile-class weapons.
Pyongyang is banned from firing ballistic missiles under UN Security Council resolutions.
U.S. Defense Secretary Mark Esper described North Korea's missile testing "disappointing", but he said he didn't "regret trying to take the high road, if you will, and keep the door open for peace and diplomacy if we can move the ball forward", CNN reported. The first incident happened in September, according to South Korea's military.
The series of shorter-range missile launches in recent months has improved North Korea's ability to make solid-fuel ballistic missiles that are easier to move, hide and fire than many of its liquid-fuel versions.
In early October, it conducted its first underwater launch of a ballistic missile in three years.
The US and South Korea meanwhile said the murder was orchestrated by Pyongyang.
Last month, Kim Jong Un also demanded that South Korea remove what he called its "unpleasant-looking" resort facilities from Mount Kumgang, which was the site of a suspended joint tourism project.
On Monday, North Korea said leader Kim visited a front-line islet and ordered artillery troops there to practice firing near the sea boundary, the scene of several bloody naval clashes between the Koreas in past years.
Prime Minister Dr Mahathir Mohamad has hinted at a further thawing of relations between Putrajaya and Pyongyang, over a year after he said Malaysia would reopen its embassy in North Korea, shuttered in the wake of the diplomatic row sparked by the assassination of North Korean leader Kim Jong Un's half-brother in Kuala Lumpur.
North Korea has maintained a self-imposed moratorium on long-range missile and nuclear tests that President Donald Trump has suggested would be a red line for the United States.
Some experts say North Korea may restart those major weapons tests if the United States fails to meet the deadline. In recent weeks his top cadres have been quoted in official media as expressing frustration by what they saw as USA inflexibility.
Negotiations have been gridlocked since a second summit between the pair in Hanoi in February collapsed without a deal.
Earlier this month, the United States and South Korea said they would postpone a joint military exercise after the North deemed merely scaling back the exercises as insufficient.