Watching a summit thought unimaginable just months ago, South Koreans raised both hope and concerns for future relations with the "brethren" North, which has been separated from the South since the 1950-53 Korean War.
But Rocky Kim says Trump failed by not pushing him to commit to a timeline for getting rid of nuclear weapons, calling it a "painted peace to show to the world".
"Anyone can make war - only the most courageous can make peace", Trump said.
Mr Trump's announcement, made in a press conference at the end of the historic summit with Mr Kim, could overturn longstanding USA policy and was described by experts as an "astonishing" concession.
Yu said China supports ongoing talks - whether they are bilateral or multilateral - but China will be a major player regardless of the form.
Kim said that human rights abuses in North Korea are "so widespread and pervasive that it is hard to pick just one" to focus on in future talks between Washington and Pyongyang, but suggested that the country's gulag system is "at the core" of violations.
Pilot rescued after Kadena-based F-15C crashes into waters off Okinawa
Air Force is also considering replacing the F-15s, worth around $36 million each, with F-16 fighting falcons by 2020. The F-15C, assigned to the 44th Fighter Squadron of the 18th Wing, crashed at approximately 6:26 a.m.
How did South Korea react?
Ahead of the summit with Kim, speculation persisted that the two sides might discuss withdrawing the US troops from the South, as Pyongyang has called for the pullout as a key signal to the end of Washington's "hostile" policy to it. -South Korea defensive military exercises has stunned our allies and our own military.
What else did they agree at the summit?
While most of the agreements confirmed to have come out of the Trump-Kim summit were pretty straightforward, advancing on the already discussed denuclearization, the meeting also ended with an announcement that the United States will suspend all joint military exercises with South Korea.
After a one-on-one meeting, followed by wider talks with advisers and a working lunch, they presented their agreement.
In his second and last telephone conversation with Mr Trump in just two days, Moon offered to discuss a joint excavation programme with North Korea to recover the remains of U.S. soldiers killed or captured in the Korean War, Cheong Wa Dae said earlier.
Most of the remains are located in mass graves, Joe Davis, a Veterans of Foreign Wars spokesperson, told TIME.
"Christians, yes", said Trump.
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Asked about the issue after the meeting, President Trump said he'd been lobbied about the issue even as a presidential candidate.
At Seoul Station in the morning, busy passers-by stopped to watch the two leaders exchange the historic first handshake and opening remarks on television screens.
"Kim Jong Un clarified the stand that if the U.S. side takes genuine measures for building trust in order to improve the DPRK-U.S. relationship, the DPRK, too, can continue to take additional good-will measures of next stage commensurate with them", the KCNA said.
On conservative Fox News and among Mr Trump's core supporters, the president was lauded for a historic diplomatic breakthrough.
Republicans in Congress have been more measured.
That four-point agreement had scant detail about how to verify any steps North Korea takes toward complete and irreversible denuclearisation.
The Korean Central News Agency (KCNA) added that Trump expressed his intention to suspend all joint military drills between South Korea and the USA while talks are under way between Pyongyang and Washington. "However, Pyongyang itself, just like all of us, like Russia, China and the worldwide community in general, has always spoken of the denuclearization of the whole Korean Peninsula".
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Sanford's apparent loss makes him the latest Republican to be forced from office for his lack of fealty to the president. Tweeting from the plane bringing him home from Singapore, he declared Sanford "very unhelpful" in advancing his agenda.