Hanoi: US President Donald Trump and Kim Jong-un have shaken hands again in front of the world's cameras before a second summit that will seek to break a deadlock in denuclearisation talks.

Greeting Trump at Hanoi's colonial Metropole Hotel, Kim said the 261 days since their first historic summit in Singapore had required "agonising effort and patience".

"But here we are today, I hope we can make fruitful achievements... and that gives me a hope that we will be successful this time," Kim said.

Trump replied that the first summit was "very successful" and downplayed critics. "I hope this one will be equal or greater than the first...The biggest progress is our relationship," he said.