Kim Yong-chol, vice-chairman of North Korea's ruling party executive and a veteran regime insider met with the U.S. President at the White House on Friday to deliver the letter.
Until Kim agrees to denuclearization, Trump added, the US sanctions on North Korea will remain as they are now. "I think they want to do that, I know they want to do that", he said, adding that a process like this would likely take more than one meeting.
"These talks go to the question of security and if anything that's probably most immediately paramount to Kim", he said.
Kim's arrival in Washington - in a small caravan of SUV's from NY - came a day after Secretary of State Mike Pompeo declared that he was confident negotiations with Pyongyang were "moving in the right direction". A letter being delivered to me from Kim Jong Un.
"I purposely didn't open the letter". However, his comments were the most positive from any USA official since Trump abruptly canceled the meeting last week after belligerent statements from the North.
"We talked about nearly everything". The announcement puts back on track a high-risk summit that could be a legacy-defining moment for the American leader, who has matched his unconventional deal-making style with the mercurial Kim government.
The prospect for a nuclear-free Korean Peninsula could hinge on who picks up the tab for Kim Jong Un's hotel. But there are lingering doubts on whether he will ever fully relinquish his nuclear arsenal, which he may see as his only guarantee of survival in a region surrounded by enemies.
USA defense and intelligence officials have repeatedly assessed the North to be on the threshold the capability to strike anywhere in the continental US with a nuclear-tipped missile - a capacity that Trump and other US officials have said they would not tolerate.
Despite the upbeat messaging in the United States, Kim Jong Un, in a meeting with Russia's foreign minister on Thursday, complained about the USA trying to spread its influence in the region, a comment that may complicate the summit.
When it comes to paying for lodging at North Korea's preferred 5-star luxury hotel, the United States is open to covering the costs, the two people said, but it's mindful that Pyongyang may view a US payment as insulting.
Some analysts suggest the video is part of an effort by North Korea to show its willingness to negotiate its nuclear weapons policy.
North Korea, whose nuclear ambitions have been a source of tension for decades, has made advances in missile technology in recent years but Trump has sworn not to allow it to develop nuclear missiles that could hit the United States.
Kim Yong Chol is the most senior North Korean visitor to the United States since Vice Marshal Jo Myong Rok visited Washington in 2000 to meet President Bill Clinton and Secretary of State Madeleine Albright.
At the same games, the International Olympic Committee paid for 22 North Korean athletes to travel to the event.