Donald Trump and  Kim Jong-un have sat down for unprecedented talks between the leaders of two long-hostile nations, as the world watches anxiously for signs of a peace deal and an agreement on the denuclearisation of the Korean peninsula.

Trump and Kim met privately from 9:05am local time for 48 minutes flanked only by their translators, then broke for a wider bilateral meeting with aides, a meeting expected to last 90 minutes, leading into lunch at 11:30am (3:30 GMT).

Before the start of the private meeting, Trump and Kim exchanged small talk in front of news photographers and television cameras, saying "We look forward to working this out together ... It will be done".

Later in the day, Trump is reportedly set to give his first post-summit interview at the Capella Hotel on Sentosa Island to Fox News' Sean Hannity, a leading Trump booster, who is in Singapore covering the summit.

Trump is scheduled for a news conference at 4pm local time.

The meeting on Tuesday between the US president and North Korea's leader, unthinkable until recent months and uncertain until June 1, is a high-stakes and politically risky venture into summit diplomacy by two unpredictable personalities who have famously exchanged personal insults and threats of war.

US officials and the North Korean state news agency struck a hopeful tone as the meeting approached, while negotiators from both countries met privately in the last hours to iron out agreements, such as over the definition of denuclearisation and the terms under which Pyongyang might agree to dismantle its nuclear arsenal.

Early on Tuesday, just a few hours before his meeting with Kim, Trump wrote on Twitter that "meetings between staffs and representatives are going well and quickly". He quickly cautioned, however, that "we will all know soon whether or not a real deal ... can happen".

His comments echoed those of US Secretary of State Mike Pompeo who said on Monday talks between the countries were "moving quite rapidly and we anticipate they will come to their logical conclusion even more quickly than we had anticipated". 

"I'm very optimistic that we will have a successful outcome from our meetings tomorrow," he said.

The North's state-run Korean Central News Agency (KCNA) heralded the summit as part of a "changed era."

"Wide-ranging and profound views on the issue of establishing new DPRK-US relations, the issue of building a permanent and durable peace-keeping mechanism on the Korean Peninsula, the issue of realising the denuclearisation of the Korean peninsula and other issues of mutual concern, as required by the changed era, will be exchanged at the DPRK-US summit talks," KCNA reported in English.

DPRK stands for North Korea's formal name, the Democratic People's Republic of Korea. 

Agencies