National security adviser Shotaro Yachi made the remarks in a meeting near Tokyo with China’s top diplomat, State Councillor Yang Jiechi, on Monday.
On Monday, KCNA said the latest test follows the successful test last week of another missile that has put Hawaii and Alaska within range.
Kim Jong Un said on Sunday his nuclear-capable country was close to test-launching an intercontinental ballistic missile.
In February, North Korea launched a satellite into space, which was widely seen as a test of long-range ballistic missile.
Kim asked that the scientists and engineers make preparations for launching the satellite as soon as possible.
US, European and Chinese seismological agencies reported that the tremor was recorded at 0030 GMT.
The missile was fired at around 5:30 am from near the coastal city of Sinpo.
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Kim Jong Un says the country now has the capability to attack US interests in the Pacific.
The first missile was launched from the east-coast city of Wonsan, a South Korean official said.
The launch attempt took place at around 5:20am Seoul time, officials said.
Concern has been growing that North Korea could soon conduct another nuclear test.
Yonhap said the failed launch appeared to be a Musudan missile with a range of more than 3,000 km.
Yonhap news agency said a mobile launcher was spotted carrying up to two Musudan missiles.
Leaders recommitted their countries to each other’s defence and warned they could take further steps.
The projectiles fired on Monday flew for 200 km and landed in waters east of North Korea.
The missile was launched from north of the capital, Pyongyang, flying across the peninsula and into the sea.
Dozens of South Korean trucks were already returning across the border earlier today.
