HANOI, Feb 28 - U.S. President Donald Trump and North Korean leader Kim Jong Un on Thursday began talks on the second day of their second summit, with both sides expressing hope for progress on improving relations and the key issue of denuclearisation.

Trump and Kim met in the Vietnamese capital, Hanoi, on Wednesday for a first, brief round of talks and a dinner, and both appeared upbeat, with Trump saying he was satisfied with the pace of negotiations despite some criticism they were not moving quickly enough.

"I've been saying very much from the beginning that speed is not that important to me. I very much appreciate no testing of nuclear rockets, missiles, any of it, very much appreciate it," Trump told reporters as he and Kim sat at a round table in the French-colonial-era Metropole hotel before their session.

"We just want to do the right deal."

North Korea has conducted no nuclear or intercontinental ballistic missile tests since late 2017.

North Korean leader Kim Jong Un speaks during the one-on-one bilateral meeting with U.S. President Donald Trump at the second North Korea-U.S. summit in the Metropole hotel in Hanoi, Vietnam February 28, 2019. Photo: Reuters

Kim, asked by a reporter if he was confident about a deal, said, through an interpreter:

"It's too early to tell, but I wouldn't say I'm pessimistic. For what I feel right now, I do have a feeling that good results will come out," he said, in what was believed to be his first ever response to a foreign journalist.

"There must be people who watch us having a wonderful time, like a scene from a fantasy movie. We have so far made lots of efforts, and it's time to show them," Kim said.

Trump reiterated North Korea's potential, if a deal can be done, saying the Asian country could be an "economic powerhouse".

Despite the optimism, there's been no sign of progress on the key issue of denuclearisation at their second summit in eight months.

The two leaders have a series of meetings scheduled at the Metropole, beginning with a one-on-one session lasting 45 minutes, the White House said.

After a "joint agreement signing ceremony" Trump plans a news conference at 3:50 p.m. (0850 GMT).

The White House has given no indication of what the signing ceremony might involve, although the two sides' discussions have included the possibility of a political statement to declare the 1950-53 Korean War over.

They have also discussed partial denuclearisation measures, such as allowing inspectors to observe the dismantling of North Korea's Yongbyon nuclear reactor, U.S. and South Korean officials say.

U.S. concessions could include opening liaison offices or clearing the way for inter-Korean projects, but critics say Trump risks squandering vital leverage if he gives away too much, too quickly.

U.S. President Donald Trump is pictured during the one-on-one bilateral meeting with North Korean leader Kim Jong Un at the second North Korea-U.S. summit in the Metropole hotel in Hanoi, Vietnam February 28, 2019. Photo: Reuters

Pressure

The Hanoi summit was Trump's second with Kim since an inconclusive meeting in Singapore in June that produced much fanfare but little substance and there had been little sign of concrete progress since.

The U.S. president nevertheless appeared upbeat with Kim even as his former personal lawyer Michael Cohen testified at a congressional hearing in Washington, calling Trump a "conman" who knew in advance about the release of stolen emails aimed at hurting his Democratic rival in the 2016 election campaign.

Facing mounting pressure at home over investigations into Russian meddling in the election, Trump has sought a big win by trying to persuade North Korea to give up its nuclear weapons in exchange for promises of peace and development, a foreign policy goal that has confounded multiple predecessors.

Their June meeting in Singapore was the first between a sitting U.S. president and a North Korean leader. It produced a joint statement in which Kim pledged to work toward denuclearisation of the Korean peninsula and the two sides committed to establish new ties and build a permanent peace regime.

But there has been little progress since.