US President Trump shakes hands with North Korea leader Kim Photograph:( AFP )
Trump shook hands with Kim as the two leaders hoped for a "very successful" summit.
US President Trump and North Korea leader Kim Jong-un opened the second summit in the Vietnamese capital Hanoi on Wednesday.
Kim and Trump shook hands and smiled briefly in front of a row of their countries' flags at the Metropole hotel in the Vietnamese capital, Hanoi.
Trump told reporters he thought the talks would be very successful, and asked if he was "walking back" on denuclearisation, said "no".
"I am certain that an outcome will be achieved this time that will be welcomed by all people," Kim told Trump. "I will do my best to make that happen."
Trump had earlier met Kim in Singapore in June last year as the North Korean leader promised to denuclearise the Korean Peninsula, however, no real progress was reported leading several experts to claim that North Korea a was stalling.
In the run-up to this summit, Trump has indicated a more flexible stance, saying he was in no rush to secure North Korea's denuclearisation. He repeated that on Wednesday, saying while some people believed the talks should be moving more quickly, he was satisfied.
Trump has held out the prospect of easing sanctions if North Korea does something "meaningful".
The two leaders are scheduled to hold a 20-minute, one-on-one chat followed by a dinner with aides.
Trump will be accompanied by Secretary of State Mike Pompeo and acting Chief of Staff Mick Mulvaney. Kim will be joined by his top envoy, Kim Yong Chol, and Foreign Minister Ri Yong Ho.