North Korea fired what was believed to a ballistic missile on Tuesday, South Korea's military and the Japanese coastguard said.
The launch was detected about 7.27am from an inland area of North Korea towards the ocean off its east coast, South Korea's Joint Chiefs of Staff said.
The projectile appeared to have landed outside Japan's exclusive economic zone, the Kyodo news agency reported, quoting government sources in Tokyo.
The launches by nuclear-armed North Korea underscored Mr Kim's New Year's vow to strengthen the military against an unstable international situation amid stalled talks with South Korea and the US.
"The [South Korean] military is maintaining a readiness posture while closely monitoring related trends under close co-operation between [South Korea] and the US in preparation for additional launches," the joint chiefs said.
South Korean and US intelligence agencies are conducting detailed analysis for additional information, it said.
Japan's Prime Minister Fumio Kishida said North Korea's repeated missile launches were "very regrettable".
Last week, South Korean military officials cast doubts on the capabilities of a "hypersonic missile" North Korea claimed to have tested on Wednesday, saying it appeared to represent limited progress on Pyongyang's ballistic missiles.
Tuesday's launch came a day after the US mission to the UN, joined by France, Ireland, Japan, the UK and Albania, condemned last week's test.
"These actions increase the risk of miscalculation and escalation and pose a significant threat to regional stability," US ambassador Linda Thomas-Greenfield said on Monday.
Such tests not only improve the North's capabilities, but expand what it can offer illicit arms clients and dealers around the world, Ms Thomas-Greenfield said.
"[North Korea] makes these military investments at the expense of the well-being of the North Korean people," she said.
UN Security Council resolutions ban all ballistic missile and nuclear tests by North Korea, and the body has imposed sanctions over the programmes.
Ms Thomas-Greenfield repeated calls for countries around the world to enforce sanctions, and for North Korea to return to talks and abandon its missiles and nuclear weapons.
"Our goal remains the complete, verifiable and irreversible de-nuclearisation of the Korean Peninsula," she said.
The US State Department did not immediately respond to a request for comment about Tuesday's launch.
North Korea has said it is open to talks, but only if the US and others drop "hostile policies" such as sanctions and military drills.
Few observers expect Mr Kim to ever fully surrender his nuclear arsenal.
North Korea says its missile tests and other military activities are for self-defence and are similar to those regularly undertaken by other nations.