Earlier, Trump and Kim held a historic summit in Singapore and committed the United States and North Korea to establishing new bilateral relations and building a lasting peace on the Korean Peninsula.
After the summit, Trump said the process of repatriating remains would begin immediately.
Having advised Trump on national security issues for one year on the National Security Council, Bossert said that the president's words at the summit largely echoed his previous discussions with top aides. "The world has taken a big step back from potential nuclear catastrophe!" China, as North Korea's neighbor and most important trading partner, also could provide relief to Kim by throttling down sanctions enforcement on its own. The current leader's father, Kim Jong Il, was a longtime movie buff who had thousands of titles in his film collection and once led North Korea's ministry of propaganda.
World powers from China to Japan, the European Union and Russian Federation welcomed its outcome - while cautioning it was only the first step towards resolving the nuclear stand-off with Pyongyang.
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It also legitimized Kim, critics charged, feting a regime which stands accused of widespread human rights abuses.
The handshake marked the start of the summit between the leaders, and displayed a stark contrast from the insults that had previously been thrown out by both men in the months leading up to the sit-down meeting.
Trump, who starred on NBC's reality show "The Apprentice" before entering politics, told reporters he was "not concerned at all" that the film could be used as propaganda, adding, "We could use that video for other countries".
Elias-Fatile stated that the meeting which resulted to the signing of a statement by the two leaders emphasised the establishment of new relationship between them.
Kim's vows to denuclearize were reported by state media Wednesday within that context - that Pyongyang would respond to easing of what it sees as the US hostile policy against it with commensurate but gradual moves toward "the complete denuclearization of the Korean Peninsula".
Trump has said repeatedly that Tuesday's summit was only the start of a process and that the USA would not ease up pressure on the North - including a crippling sanctions regime - until its goal of North Korea's "complete, verifiable, irreversible denuclearization" is reached. American officials have typically avoided such language to describe North Korean leaders, because of the country's long record of human rights abuses and frequent threats against the US and its allies.
"We're going to have to check it and we will check it".