"We expect the DPRK to refrain from any further provocations, abide by its stated commitments, and fully implement its worldwide obligations as determined by multiple United Nations Security Council Resolutions".
Kim guided the test-fire for the new weapon from an observation post and expressed "great satisfaction" to munitions officials afterwards, said the official Korean Central News Agency (KCNA) report. That's according to a statement released on Sunday morning, by a senior North Korean foreign ministry official in charge of US affairs.
Last week, South Korea and the USA conducted preliminary sessions in the run-up to their joint summertime training.
With the 2020 presidential elections on the horizon, Trump has repeatedly downplayed the significance of North Korea's frequent missile launches, claiming these tests use "smaller ones" and not ballistic missiles despite his officials reporting otherwise, the New York Times reported.
Saturday's launch was the North's fifth test in two weeks as it protests the annual military drills under way between Seoul and Washington which always infuriates Pyongyang.
The exercise's name change, however, does not "alter its aggressive nature", Kwon stressed, saying that direct talks with Seoul are impossible in such circumstances.
Mr Trump said he is looking "forward to seeing Kim Jong Un in the not too distant future". "We should be reimbursed for it, and I've told that to South Korea".
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"It was a long letter, much of it complaining about the ridiculous and expensive exercises", the president wrote in a series of tweets.
The tests violate United Nations Security Council resolutions that ban North Korea from any ballistic missile activity.
Photographs from the weapons test released by KCNA on Sunday showed a rocket being launched from a transporter erector launcher (TEL) with a different exterior paint job from the missile fired last Tuesday or the rocket artillery the regime said it tested on July 31 and August 2.
One diplomatic source said, "Trump's top priority is to prevent a major North Korean provocation that threatens US territory, and Kim knows this, which is why he is not stepping over the line".
Trump said Kim promised the testing would stop when the exercises end. Robert Wood, US ambassador to the Geneva conference, told reporters that Washington was still committed to negotiations and the military exercises were not meant to threaten North Korea.
Pyongyang also mocked Seoul for failing to accurately assess the projectiles that it has fired in recent weeks, directly criticizing the South Korean president and defense minister.
The North Korean foreign ministry said Trump's comment "in effect recognises the self-defensive rights of a sovereign state, saying that it is a small missile test which a lot of countries do".