The rival Koreas have already agreed to hold a leadership summit in late April.
But tension eased around last month's Winter Olympics in South Korea, laying the groundwork for what would be the first meeting between leaders from North Korea and the United States, and the biggest foreign policy gamble for Trump since he took office in January previous year.
Trump at his United Nations speech, where he referred to Kim as "rocket man" in front of hundreds of diplomats. "He then endured multiple amputations without anything to boring the pain", Mr Trump said of Ji Seong Ho.
The two leaders traded insults and nuclear threats past year, and then cooled their rancor as US ally South Korea prepared for the Winter Olympic Games at Pyeongchang in February.
Mr Kim's apparent offer to discuss denuclearisation of the Korean peninsula in exchange for what South Korean officials have described as "security guarantees" looks like little more than a cynical ruse.
July 2017: Following another long range missile test, Mr Trump takes a measured approach, and accuses the country of isolating itself with the threatening lunches.
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Both men are political novices. But his blind self-confidence carries a risk. Unless Trump rejects that view, it will be essentially impossible for the administration to develop a workable plan for the summit.
Since 1950 US military personnel have been stationed on the Korean peninsula. I understand that if the past is an indication of the future, North Korea will be all talk and no action. Mr Trump reaffirmed the US' commitment to defending Japan against a North Korean threat. In addition to suspending its nuclear program, Pyongyang would also have to decommission facilities and transport nuclear materials overseas.
The International Atomic Energy Agency, which is the UN's nuclear watchdog, voiced hope that the summit would produce "concrete progress" and a resumption of nuclear inspections which have been suspended for years.
But Washington has been repeatedly let down before.
"They have often led to concessions being made to North Korea in return for talks".
Basketball star Dennis Rodman, who has visited North Korea, cheered Trump's move.
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The summit could also break down if the USA decides that full denuclearization seems unlikely.
At the same time, Mr. Xi sounded a note of caution, saying he hoped "all parties concerned will show goodwill and avoid doing anything which might affect or interfere with the improving situation on the peninsula". They have his poll numbers at 42% which is still higher than Obama's at this time while many others have him at 50%. He is expected to have tricks up his sleeve to appease Trump, such as a concrete timeline for phasing out missiles and nuclear arms.
The stunning announcement was the culmination of a diplomatic whirlwind that began with the invitation of a North Korean delegation to attend the Winter Olympics in Pyeongchang, South Korea.
Meanwhile, Washington is short of diplomatic talent. The key question will be what North Korea has to do to make that summit actually happen? Trump could settle for an agreement marking less than a breakthrough if he can keep the North from building ICBMs for now.
Trump's chief diplomat, Secretary of State Rex Tillerson, speaking to reporters Friday during his weeklong swing through Africa, said the meeting came about because of a "dramatic" change in posture by Kim Jong Un.
In briefings after the surprise announcement of a summit - which would be the first ever meeting of leaders of the two countries - United States officials made no mention of possible concessions that Trump might offer, other than saying that severe sanctions would stay in place until North Korea took verifiable steps to dismantle its nuclear weapons programme.
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