Hours later, Kim branded Trump as "deranged".
Mr Ri is due to give a speech at the UN General Assembly on Friday, according to Yonhap news agency.
North Korea has twice successfully tested an intercontinental ballistic missile, fired intermediate-range ballistic missiles over Japan, and tested a suspected hydrogen bomb.
Trump not only called Kim Jong Un "Rocket Man", a phrase he's used lately to describe the dictator, but he added the epithet "Little". China's central bank has ordered all the financial institutions to apply the United Nations sanctions following the recent complaints from the USA administration that Beijing is exposing too many loopholes for North Korea.
Pyongyang conducted its sixth and most powerful nuclear test on September 3, claiming it had tested a hydrogen bomb that could be loaded into an intercontinental ballistic missile.
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USA analysts now estimate that North Korea may have as many as 60 nuclear weapons , according to a Washington Post report. In a one-and-only such test in 1962, the USA launched a nuclear-tipped ballistic missile from a submerged submarine.
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" Iran is continuing missile development, missile development that could be paired with a nuclear program later", McMaster said. In an obvious response to Trump's "America First" mantra, Gabriel said the world needs more cooperation, less "national egoism".
However, the sanctions package is not as severe as Trump had previously threatened, as he had stated before that he would target any foreign government doing business with North Korea. "Together with China we'll continue to strive for a reasonable approach and not an emotional one like when children in a kindergarten start fighting and no-one can stop them", he said.
"North Korea's nuclear program is a grave threat to peace and security in our world, and it is unacceptable that others financially support this criminal, rogue regime", Trump said in a press briefing with the leaders of South Korea and Japan.
The UN speech came just hours after US Air Force bombers, escorted by fighter jets, flew in worldwide airspace over waters east of North Korea. "We have developed strong allies and strong alliances internationally".
He stressed that North Korea's nuclear drive was aimed at developing a "war deterrent" and declared that his country was a "responsible nuclear weapon state".
China's Earthquake Administration said the quake was not a nuclear explosion and had the characteristics of a natural tremor.