Trump said that Kim had "kept his word" and there had been "no nuclear testing, no major missile testing" since their recent negotiations.
The agreement signed by Kim and Trump in Singapore "is in danger of being a blank sheet of paper because the U.S.is turning a blind eye to its implementation", KCNA said. North Korea has denied this.
"We have a very good relationship together", Trump said. "That's very important to me", Trump said. "But in the meantime, we have our hostages back, the remains keep coming back, we have a relationship". Trump even said the unlikely pair "fell in love" over the correspondence. But in the past they have served as vehicles to plan - or cancel - summits between the two leaders.
However, this latest note from Kim did not propose any future meetings, signalling the diplomatic process may have reached a dead end.
Bob Baer, a former CIA case officer and CNN analyst, said that it is not a surprise that Trump would deny the USA has used spies to collect intelligence on North Korea.
She was seen smiling broadly and shaking hands with South Korean officials before sitting across a table and handing over a purple folder containing the condolence letter.
The two sides haven't held working-level talks in months and North Korea hasn't responded to multiple requests to restart the negotiations, according to US officials.
Biegun's previous counterpart, Kim Hyok Chol, is alive but he is being investigated for his role in the failed Hanoi summit.
Trump and Kim agreed at the first U.S.
The launches are a potential embarrassment for Trump, who has long pointed to a lack of North Korean missile and nuclear tests as evidence his talks with Kim are succeeding.
Susan Rice, who was national security adviser for Trump's Democratic predecessor, Barack Obama, tweeted her reaction to the remarks: "America, this tells you all you need to know about our so-called 'Commander-in-Chief'".
Lee's husband is best remembered for his policy of engagement with the nuclear-armed North that led to a historic summit with Kim Jong-Un's late father Kim Jong-Il in 2000. I view it as a man - perhaps he wants to get attention, and perhaps not.
Both sides have said they are open to talks but that the other side needs to change their policy. Fifield says Kim Jong Nam usually met his handlers in Singapore and Malaysia, citing a source with knowledge of the intelligence.
A new biography of Kim published in the U.S. on Tuesday said Kim Jong-nam, who lived in exile most of his life, had been recruited by the Central Intelligence Agency.
There is some speculation he met with intelligence officials in those countries as well.
North Korean leader Kim Jong Un's sister met South Korean officials on their heavily defended border on Wednesday to deliver flowers and her brother's condolences over the death of a former South Korean first lady.