If the test -- which came as the United States prepared to mark its independence day on the Fourth of July -- represents an intercontinental ballistic missile (ICBM) it would force a recalculation of the strategic threat posed by Pyongyang.
The North has long had ambitions to build a rocket capable of delivering an atomic warhead to the continental United States - something that Trump has vowed "won't happen".
Analysts say the isolated, impoverished country has made great progress in its missile capabilities in the years since the ascension to power of young leader Kim Jong-Un, who has overseen three nuclear tests and multiple rocket launches.
In response to the latest, Trump asked on Twitter: "Does this guy have anything better to do with his life?"
There are still doubts whether the North can miniaturise a nuclear weapon sufficiently to fit it onto a missile nose cone, or has mastered the technology needed for it to survive re-entry into the Earth's atmosphere.
The United Nations has imposed multiple sets of sanctions on Pyongyang over its weapons programmes, which retorts that it needs nuclear arms to defend itself against the threat of invasion.
The "unidentified ballistic missile" was fired from a site in North Phyongan province, the South's Joint Chiefs of Staff said in a statement, and came down in the East Sea, the Korean name for the Sea of Japan.
US Pacific Command confirmed the test and said it was a land-based, intermediate range missile that flew for 37 minutes, adding the launch did not pose a threat to North America.
It was estimated to have reached an altitude of more than 2,500 kilometres, Japan said.
"That's it. It's an ICBM," responded arms control specialist Jeffrey Lewis on Twitter. "An ICBM that can hit Anchorage not San Francisco, but still."
David Wright, of the Union of Concerned Scientists, wrote on the organisation's allthingsnuclear blog that the available figures implied the missile "could reach a maximum range of roughly 6,700 km on a standard trajectory".
The device came down in the Sea of Japan within the country's exclusive economic zone, the defence ministry said in a statement, waters extending 200 nautical miles from its coast.
Prime Minister Shinzo Abe told reporters: "This launch clearly shows that the threat has grown."
The US, Japan and South Korea will hold a summit on the sidelines of this week's G20 meeting on the issue, he added. "Also I will encourage President Xi Jinping and President Putin to take more constructive measures."
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