"The United States and its partners remain gravely concerned about the degree of UN Security Council resolution violations that are occurring in relation to North Korea's import of refined petroleum products", the USA mission to the UN wrote in the report.
On Tuesday, Trump said that he had received a letter from Kim, the first the USA and North Korean leaders have exchanged since January.
While she became the first member of the ruling family to visit Seoul and accompanied Kim Jong Un in his summits with Trump and Chinese President Xi Jinping, she's also performed mundane tasks, such as helping the leader extinguish a cigarette during a train stop in China.
The meeting followed another letter sent by Kim to Trump on Monday, marking a slight thaw in North Korea's position since the Hanoi summit. Trump added that he had seen the "information about the Central Intelligence Agency in regard to his brother or half-brother, and I would tell him [Kim Jong-un] that would not happen under my auspices".
Moon said such a meeting would be "desirable" but added that it was up to Kim Jong Un to decide.
Reclusive North Korea and the rich, democratic South are technically still at war because their 1950-53 conflict ended in a truce, not a peace treaty.
It's still unclear if the meeting could lead to the resumption of talks.
Trump, who has tried to convert what he feels is a warm personal relationship with Kim into a diplomatic breakthrough, gave no details, but repeated that he believed North Korea had "tremendous potential".More news: Iran's Zarif calls oil tanker incidents 'suspicious', wants regional talks
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A Security Council diplomat told reporters late Wednesday that the US, along with 25 other countries, had complained to the U.N. Security Council sanctions committee monitoring the country's compliance with sanctions slapped on the country in 2017.
White House national security adviser John Bolton is also backing a new summit.
He was killed in February 2017 after two women smeared nerve agent on his face in Kuala Lumpur International Airport.
The United States says North Korea needs to make verifiable progress toward giving up its nuclear weapons before any sanctions are eased, while North Korea says the United States has done nothing to reward steps already taken.
The brothers remained estranged as adults, and in 2013 the younger Kim executed Chang Song-thaek, his aunt's husband, who was said to be close to Jong-nam.
In the letter, whose contents were partially made public at the funeral ceremony of Lee Ho, praised the first lady as well as her husband the late president Kim Dae-jung for steering Seoul to growth and unity amid hardships and troubles.