Donald Trump has told North Korean dictator Kim Jong-un they have a "great relationship" and predicted their summit in Hanoi could be "even greater" than their historic meeting last year.
The two leaders smiled and shook hands for the cameras before they held a meeting at the Sofitel Metropole Hotel in the Vietnamese capital before the two leaders and a small entourage had dinner together.
The photo opportunity took place before a dozen US and North Korean flags.
The meeting and dinner have now ended and Trump has returned to his hotel to prepare for their official and more substantial meeting on Thursday.
Trump appeared to joke with Kim as they sat down to dinner.
"Boy, if you could've heard that dialogue," he said of the media. "What you would pay for that dialogue. It was good."
In brief remarks before the dinner, Trump told reporters he was "satisfied" with North Korea's path towards denuclearisation.
"We made a lot of progress," Trump said of their first summit in Singapore. "I think the biggest progress was our relationship, is really a good one."
"It is an honour to be with Chairman Kim. It's an honour to be together in a country, Vietnam, where they have rolled out the red carpet and they are very honoured to have us," Trump said as the two leaders sat alongside each other.
"It's great to be with you. We had a very good first summit … Some people would like it to go quicker, but I'm satisfied. You're satisfied. We want to be happy with what we're doing."
Kim said "a lot of obstacles" had to be overcome for the summit to occur but he was "confident there will be a good result".
The past few months had seen a lot of patience and effort, he said.
The pair took turns praising each other, with Kim saying Trump meeting him was a "courageous decision".
Kim smiled as Trump shook and grasped his hand as they were photographed by media from around the world.
"I am certain that a great 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."
Kim signed a loose promise to work "towards the denuclearisation of the Korean peninsula", but the two sides have since disagreed over what that actually meant.
"We came all the way to Hanoi to meet again," Kim said.
"When I think about, it was a period where we needed more thought, effort and patience than at any time," apparently referring to the past eight months and the disagreements.
The leaders then headed into the dinner, Trump accompanied by secretary of state Mike Pompeo and his acting chief of staff Mick Mulvaney, while Kim has the vice chairman of the Worker's Party of Korea Kim Yong Chol and the minister of foreign affairs Ri Yong Ho with him.
According to media present, as the two parties sat down to eat, all crammed around a relatively small table, Trump said "our relationship is a very special relationship" with Kim later adding he and Trump "shared a lot of interesting stories".
Trump thinks he can convince North Korea's Kim Jong-un his country could thrive economically if he abandons his quest to become a nuclear power.
"We'll see what happens, but he wants to do something great," the US President said before the meeting, adding that Kim could use Vietnam - their hosts for their second summit - as a model for economic revival.
"If you look at what you've done in a short time, he can do it in a very, very rapid time - make North Korea into a great economic power."
There is speculation in Hanoi Kim expects to return home with economic rewards, including partial sanctions relief. But there's growing worry among analysts that Trump, who will be desperate for an agreement, will give Kim too much and get too little in return - a peace declaration for the Korean War that the North could use to eventually push for the reduction of US troops in South Korea or sanctions relief that could allow Pyongyang to restart economic projects with the South.
Critics of Trump insist he must first get real progress on North Korea abandoning its nuclear weapons before giving away important negotiating leverage too soon.
The two leaders will participate in a "social dinner" in the city's Metropole Hotel, joined by two guests and their respective interpreters. Before the dinner they are expected to have a 20-minute one-on-one conversation.
The high-stakes meeting will pick up where the Singapore summit last June left off, with the US likely to seek reassurances from North Korea that it is committed to denuclearisation.
There have been reports already that Kim is the one pulling the strings and dictating everything from where the summit was held and where the US media centre could be.
CNN reported the US wanted the summit to be held in Da Nang, which already had secret service clearance for APEC.
But Kim insisted it be held in the country's capital of Hanoi. He also insisted on taking an arduous 3200-kilometre train journey from Pyongyang to Vietnam — a trip that lasted two and a half days.
Flying would have been much shorter, of course, and would have caused far less disruption to Vietnam's roads and rails.
It was also reported that a North Korean official was demanding Vietnamese security and staff tell journalists in the lobby not to photograph Kim or the scene around him.
Earlier on Wednesday, Trump arrived at Vietnam's Presidential Palace to meet with the country's top officials.
He met with Vietnamese President Nguyen Phu Trong for a photo op and a meeting, where he praised the "thriving" country and the ties between the two countries.
He also described Vietnam as a "good example of what could happen" if North Korea was to denuclearise.
"We (Trump and Kim) both felt very good about having this very important summit in Vietnam because you really are a good example of what can happen," he told Vietnamese officials. He also said he was "very proud" of what Vietnam had accomplished economically.
Trump later joined Prime Minister Nguyen Xuan Phuc, and the pair walked past a line of young children waving US and Vietnamese flags.
At one point, Trump stopped and smiled at the children, before waving the flags at the camera.
Sitting down for bilateral talks, the two leaders congratulated each other's economic performance.
Trump credited Vietnam's "tremendous progress" under Nguyen, since he last visited the country in 2017. He also praised its military equipment.
- With AP