Kim Jong Un Thursday raised the prospect of a permanent US diplomatic presence in Pyongyang, as President Donald Trump said he was in "no rush" for a speedy deal over North Korea's nuclear programme.

The North Korean leader said he would welcome the opening of a US liaison office in his capital.

It would be an initial step on the road to normalising diplomatic ties between two countries on opposite sides of the Korean War, which is technically still not over.

Asked about the possibility of a liaison office -- below the level of an embassy -- in between talks sessions on the second day of the Hanoi summit, Kim told reporters: "I think it is something that is worth welcoming."

For his part, Trump said the idea was a "great thing".

The two leaders are holding their second summit in eight months, with analysts warning they must come up with more concrete progress than their historic meeting in Singapore in June dismissed by some as a made-for-TV show.

That encounter resulted in cosy images but only a vague commitment from Kim to "work toward complete denuclearisation of the Korean peninsula". Diplomacy has since stalled amid disagreements on what that actually means.

As they sat down for Thursday's formal discussions in Hanoi, Trump said he was in "no rush" to seal a deal and that "speed was not that important" to him as long as the North's pause in missile and nuclear testing continued.

"I can't speak necessarily for today, but I can say that this, a little bit longer-term, and over a period of time, I know we're going to have a fantastic success with respect to Chairman Kim and North Korea," said Trump.

Trump again touted the possibility of impoverished North Korea becoming an "economic powerhouse" if it gave up its nuclear arsenal -- an outcome analysts say is extremely unlikely.

Kim said he would not be sitting down with Trump if he were not ready to denuclearise but stressed that they were still thrashing out the concrete details.

The Pyongyang strongman is looking for relief from sanctions imposed on the North because of its weapons programmes, which saw tensions soar in 2017 before a wave of detente.

He said there were "people who hold a sceptical view of our meeting" but pledged to seek "great, ultimately good results".

"I think watching us have a great time will be like watching a scene from a fantasy movie," he added.

The North maintains total control over every aspect of Kim's domestic appearances, but he several times answered shouted questions from foreign reporters -- believed to be unprecedented.

The state-run Rodong Sinmun newspaper plastered photographs of their first Hanoi handshake on Wednesday over its front page, one of them appearing to show Trump bowing slightly as he took Kim's hand.

- Poolside stroll -

The two men have again displayed outward signs of an unlikely diplomatic bromance in Hanoi, clasping hands and appearing to share jokes on Wednesday.

Looking relaxed but appearing to say little, they indulged in a poolside stroll Thursday around the gardens of the luxury Metropole Hotel, a Colonial-era building that has played host to stars ranging from Charlie Chaplin to Brad Pitt.

It echoed a garden walkabout in Singapore, where the two men bonded over Trump's hulking car -- the "Beast" -- with the US president allowing the younger man a glimpse inside.

It was a far cry from the height of missile-testing tensions in 2017 when Trump slammed Kim as "rocket man" and the younger man branded the American president a "mentally deranged US dotard".

The summit was "pageantry for Trump and brings Kim more credibility on the world stage as a responsible, rational actor", the Stimson Center's David Kim told AFP.

"But I would define success in terms of outcomes. A decent outcome if we can get some concrete and verifiable commitments toward denuclearisation," he said, although the US would have to "trust but verify".

But scandal back home in Washington threatens to distract Trump with his former personal lawyer and fixer Michael Cohen calling him a "racist" and a "conman" during a congressional hearing.

The president already showed he had the testimony at the back of his mind when he tweeted about it before his first meeting with Kim, saying Cohen -- who has been sentenced to three years in jail -- was "lying in order to reduce his prison time".

In Hanoi, in addition to relief from biting sanctions, Kim is also seeking security guarantees for him and his regime.

One carrot could be a declaration on the Korean War, which ended in 1953 with an armistice, not a formal peace treaty. Asked about that before Wednesday's dinner, Trump merely replied: "We'll see."

In return, Kim might pledge to destroy North Korea's decades-old Yongbyon nuclear complex, which has long been at the heart of Pyongyang's atomic development but remains shrouded in secrecy -- and North Korea has promised to mothball it twice before.

In Vietnam, Trump has frequently pointed to the recent history of the host country -- once a war-torn foe of the United States, now enjoying an economic boom with growth of more than seven percent.

Ahead of the talks, he hailed Kim as a "friend" and said North Korea could enjoy an "AWESOME" future if it gave up its nuclear weapons.

Source: NATIONAL NEWS AGENCY