Smiles from Kim as Trump speaks of North Korea's 'unlimited potential' at their second summit

It was smiles all round as President Donald Trump and North Korean leader Kim Jong Un exchanged greetings at their second summit in Hanoi, Vietnam.

The two leaders exchanged handshakes, laughs and small talk at the Sofitel Legend Metropole Hanoi, where they were scheduled to meet for 20 minutes before sitting down for what the White House has described as a "social dinner".

Chairman Kim was unable to contain his excitement as Mr Trump spoke of North Korea's 'unlimited economic potential'.

Mr Trump told reporters of the meeting: "We look forward to it, we both do."

Asked whether he might formally end the Korean War, he responded: "We’ll see."

Kim was visibly excited to meet Donald Trump again. Credit: AP

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

Mr Trump said: “We’ll see what happens, but he wants to do something great.”

There has been a carnival-like atmosphere in the Vietnamese capital, with street artists painting likenesses of the leaders and vendors selling T-shirts emblazoned with their faces.

It stands in contrast to the serious items on the agenda: North Korea’s pursuit of nuclear weapons and peace on the Korean Peninsula.

Speaking earlier to his Vietnamese hosts, Mr Trump said: “We have a very big meeting planned tonight as you know, with North Korea, Chairman Kim, and I think it may very well turn out to be very successful.”

The president hailed Vietnam as a model for North Korea to follow in his remarks to his hosts, saying: “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.”

In a tweet earlier Mr Trump said: “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, a great opportunity, like almost none other in history, for my friend Kim Jong Un. We will know fairly soon – Very Interesting!"

President Donald Trump waves a Vietnam flag as he meets with Vietnamese prime minister Nguyen Xuan Phuc Credit: Evan Vucci/AP

Last year’s meeting between the two leaders in Singapore was a historic encounter which had followed sustained and personal insults between the pair over Pyongyang’s nuclear programme.

With tests halted since the thaw in relations, Mr Trump hopes for more progress on denuclearisation from Mr Kim.