The North Korean leader also described Pukguksong-2 as a "successful strategic weapon", with a "very accurate" hit rate.
U.S. Pacific Command said it tracked the missile until it landed into the sea.
The Pukguksong (Polaris)-2 is a land-based version of a submarine-launched missile.
South Korea said the missile flew about 500 kilometers (300 miles) from an area near Pukchang, in western North Korea. It reached an altitude of 560 kilometers (347 miles), the official said, speaking on condition of anonymity, citing office rules.
USA and South Korean officials and experts believe the North is several years away from having such a capability.
The official Korean Central News Agency said dynastic leader Kim Jong Un had deemed the launch a success and that more would be launched in the future.
The February launch, the North's first missile test after Trump took office, alarmed neighbours because solid-fuel missiles can be fired more quickly than liquid-fuel missiles, which need to be fueled before launch and require a larger number of vehicles, including fuel trucks, that could be spotted by satellites.More news: Callers threaten Texas lawmaker who seeks Trump impeachment
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South Korea has been struggling to fill the gap with promotional campaigns to attract more visitors from other countries, mainly from Japan and those in Southeast Asia.
"The Trump administration would be well advised to lend an ear to the voices of concern that are heard from the USA and the global community", the North's Minju Joson newspaper said in a commentary Sunday.
The United States and South Korea have said the deployment is aimed purely at defending against any threat from North Korea, which experts have thought for months is preparing for what would be its sixth nuclear test in total. "Hopefully, they will get the message that the pathway of continuing their nuclear arms program is not a pathway to security, or, certainly, prosperity". The ongoing testing is disappointing.
The complex atmospheric re-entry technology is key to ensuring the warhead is able to withstand the vibrations and heat of the flight's terminal phase before the impact.
South Korea held a National Security Council meeting after the launch, and its Foreign Ministry said the launch "throws cold water" on efforts to ease tensions on the peninsula. In the recent past, North Korea did target practice for this goal, which prompted Japanese Prime Minister Shinzo Abe to place his country under the highest possible alert. He vowed to bring up the issue at this week's G-7 summit in Italy.
Britain's United Nations ambassador, Matthew Rycroft, said it is vital that the Security Council respond to the latest provocation quickly with "further substantive significant measures".
He said a new resolution is being negotiated and council members are expected to discuss it during Tuesday's closed consultations.
The fresh North Korean test was again carried out in violation of UN Security Council (UNSC) resolutions.
If the missile launch is confirmed it would be Pyongyang's eighth missile test this year.