Donald Trump and Kim Jong Un meet in Hanoi

US President Trump shook hands with Kim Jong-un on Wednesday night to kick off their second summit gathering, greeting the North Korean leader in a one-on-one exchange before a formal dinner that will include top aides to both leaders.

“I thought the first summit was a great success,” Trump said as he sat beside Kim before a room crowded with reporters. “And I think this one hopefully will be equal or greater than the first.

The two leaders have claimed a personal chemistry with each other that belies the daunting challenge they will face Thursday, when Trump will try to get Kim to commit to specific steps toward denuclearization during a day of meetings.

Trump said he thought this latest meeting would be "very successful".

Earlier, he tweeted in praise of the host country on Wednesday morning, writing: "Vietnam is thriving like few places on earth. North Korea would be the same, and very quickly, if it would denuclearize."

"The potential is awesome," he added.

Their first encounter was scheduled to be a 20-minute one-on-one meeting. It will be followed by dinner with their aides, according to the White House.

The two leaders will attend a series of meetings together on Thursday, but their exact agenda is unknown.

It's expected that any major events - the signing of agreements or significant press conferences - will take place on Thursday.

The Hanoi meeting is expected to build on the groundwork of what was achieved at the Singapore summit last June.

That meeting produced a vaguely worded agreement, with both leaders agreeing to "work towards denuclearisation" - though it was never made clear what this would entail.

Little diplomatic progress was made following the summit. This time round, both leaders will be very conscious of the need to answer their critics with signs of concrete progress.

However, Trump appeared to be managing expectations ahead of the summit, saying he was in "no rush" to press for North Korea's denuclearisation.

"I don't want to rush anybody. I just don't want testing. As long as there's no testing, we're happy," he said.

Washington had previously said that North Korea had to unilaterally give up its nuclear weapons before there could be any sanctions relief.