Trump described the letter as a "very nice note" and said, "Great progress being made!"
Mr. Trump and Mr. Kim met for the first time in Singapore to discuss the relations between their nations and potential denuclearization June 12.
"I firmly believe that the strong will, honest efforts and unique approach of myself and Your Excellency Mr. President aimed at opening up a new future between the DPRK and the US will sure surely come to fruition", Mr Kim writes.
"I extend my conviction that the epochal progress in promoting DPRK-US relations will bring our next meeting forward".
The US military also announced that 100 wooden coffins had been dispatch to Panmunjom to receive the remains, although repatriation has yet to take place.
Umtiti hails France pal Pogba: A real leader on and off pitch
The 2018 FIFA World Cup Finals are set, with France and Croatia ready to face off July 15 for the ultimate title in soccer . Many Twitter fans echoed Pogba's sentiments and praised the midfielder for taking a moment to think of the rescued boys.
Last week, North Korea accused the U.S. of using a "gangster-like" tactics to push it towards nuclear disarmament after a fresh round of high-level talks.
But what can't be denied is that Trump's decision to end the annual US/South Korea "war games" (long used by the DPRK to justify its nuclear defence program), and his statement that "yesterday's conflict does not have to be tomorrow's war", elevated Kim's isolated regime from enemy to potential friend.
"We will be ready", Mr Nauert said.
The letter is dated July 6, 2018.
The US president shared the missive from the North Korean dictator on Twitter Thursday.
South Korean officials later said the meeting would be rescheduled for July 15, but that was after USA negotiators arrived Thursday at the militarized border between the two Koreas and were kept waiting, the Yonhap News Agency reported, citing diplomatic officials it didn't identify.
Elon Musk Offers To Help Thai Officials Rescue Trapped Soccer Team
One of Mr Musk's enterprises is Boring Co, which digs tunnels for transport systems and has advanced ground-penetrating radar. Mr Musk has also been engaged in a Twitter spat over media coverage of Tesla , in particular with CNBC and Business Insider.
While the American officials clearly thought a meeting was scheduled, Secretary of State Mike Pompeo had previously indicated that the details hadn't been settled before he left North Korea on Saturday. Although Pompeo called the meetings "productive", North Korea said the lack of emphasis on security guarantees was "regretful".
The Defense Department estimates there are up to 5,300 sets of US service member remains still somewhere in North Korea.
North Korea proposed to reschedule the meeting for Sunday.
Trump has sought to cast his summit with Kim as a major victory, although reports have suggested North Korea is continuing with its nuclear programme and promises of "denuclearisation" remain vague.
The US later said that North Korea had offered to meet on 15 July.
World's largest mobile phone factory opens outside Indian capital
The South Korean President is on a three-day visit to India, having arrived in New Delhi on Sunday evening. The leaders took the Blue Line from Mandi House to reach Noida for inaugurating a Samsung facility there.
- England captain Harry Kane hurt by loss to Croatia
- Kylie Jenner on track to be youngest self-made billionaire by age 21
- Kylie Jenner reveals she Got Rid of all her Lip Fillers
- Wimbledon 2018: Serena Williams Says 'It's Crazy' After Entering 10th Final
- 'Shame on you'- Donald Trump's not-so-welcoming welcome to the UK
- This Won't Be Kavanaugh's First Knock-Down, Drag-Out Confirmation Fight
- Thanos Did Nothing Wrong Subreddit Bans Half Its Subscribers
- Lawyer: Stormy Daniels' arrest at strip club was part of sting operation
- Trump to Appoint Extreme Ideologue to the Supreme Court
- When Donald meets Vladimir - the neophyte and the black belt