US President Donald Trump and North Korea's Kim Jong-un — affable leaders of hostile nations — opened their second summit on Wednesday with hopeful words and a private chat before sitting down for dinner and further talks about North Korea's pursuit of nuclear weapons.

The two exchanged smiles and a warm handshake in front of a phalanx of alternating American and North Korean flags. They posed for cameras before disappearing for their private tete-a-tete, similar to one they had at their first historic meeting last year in Singapore.

'We made a lot of progress,' Trump said of their first summit. 'I think the biggest progress was our relationship, is really a good one.'

Asked if this summit would yield a political declaration to end the Korean War, Trump said: 'We'll see.'

Kim said he was 'confident of achieving the great results that everyone will welcome.'

The venue, the colonial and neoclassical Sofitel Legend Metropole in the old part of Hanoi, came with a bit of irony.

Trump earlier made the case that North Korea could thrive economically like Vietnam if the North ends its pursuit of nuclear weapons.

Trump said: 'We'll see what happens, but he wants to do something great.'

The two leaders are to meet again on Thursday for a formal meeting on Kim's advancing nuclear programme.

They met for the first time in Singapore last June, and that meeting ended with Kim pledging to work toward 'complete denuclearisation of the Korean Peninsula.'