Singapore – 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 United States 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.

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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.

Accompanied by Singaporean cabinet ministers, Kim made an evening tour of sites in the city-state’s waterfront on the eve of the summit [Vivian Balakrishnan’s Twitter page/via Reuters]

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

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“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.

Ultimate objective

The summit is not expected to last beyond Tuesday, with both leaders set to leave Singapore shortly after concluding their meetings.

Heading into Tuesday’s summit, the big competing items on the table came down to what by now are popular acronyms, with the US seeking the denuclearisation of the Korean Peninsula, or CVID (complete, verifiable, irreversible denuclearisation), and the North Korean leadership rejecting unilateral nuclear disarmament while seeking its survival, or CVIG (complete, verifiable, irreversible guarantee of North Korea’s security).

On Monday evening, Pompeo said that the US’ “ultimate objective” remains the complete denuclearisation of the Korean Peninsula, and that Washington is willing to provide “unique security assurances” if Pyongyang agrees to do so.

“President Trump believes that Kim Jong-un has an unprecedented opportunity to change the trajectory of our relationship and bring peace and prosperity to his country,” he told reporters.

“The fact that our two leaders are sitting down face-to-face is a sign of the enormous potential to accomplish something that will immensely benefit both of our peoples and the entire world.”

Pompeo is scheduled to immediately fly to Seoul and Beijing after the summit to brief South Korean allies and Chinese officials on the discussions, reflecting the reality than any solutions in the region will need buy-in from those nations.

Both Trump and Kim arrived on Sunday to Singapore, chosen as the site of the summit for its reputation as a safe and orderly place and the fact that it has diplomatic relations with both North Korea and the US.

Follow Tom Benner: @tgbenner

Al Jazeera’s diplomatic editor James Bays, reporting from Singapore:

This is absolutely historic. Never before have the leaders of these two countries met. These are countries that are still technically at war. However, it may be historic that they are meeting, but no one should think that this is a deal. The most we are going to get is a declaration on the start of a negotiation and this is likely going to be a long and bumpy road.

The other main observation is how fast this has moved. Today is 364 days since Otto Warmbier, a US student who the US accuses North Korea of torturing, was brought back to the US and then died. If you think of that period of last summer, it was probably the tensest period in the relationship between North and South Korea over the last 70 years. Then more nuclear tests and missile tests followed, answered by Trump with language about “fire and fury”, threatening to “totally destroy” North Korea.

We sort of know what then happened. Al Jazeera learned that the day after Trump spoke at the General Assembly in September, the North Korean foreign minister met with Antonio Guterres, the UN Secretary-General, saying the UN could send a senior UN official to Pyongyang. Weeks later Jeffrey Feldman, the then political affairs chief of the UN went to North Korea, where he said that Kim made an overture, suggesting that he should offer an olive branch by sending a delegation to the Olympics in South Korea.

This opened up diplomacy between South Korea and North Korea. The South Koreans got the CIA involved and they led the US initiative, leading to the secret meeting between Pompeo and Kim in Pyongyang at Easter, where it was revealed that diplomacy had reached a different pace. Pompeo returned to Pyongyang, on-off contacts continued, which have led to this historic summit today.

This was probably the most important day of diplomacy in the last decade, apart from one other day, when the JCPOA, or Iran deal, was finally signed in Vienna in July 2015. And that was the deal that Trump has pulled out of, setting himself an extremely high bar for the Korean diplomatic process. Trump needed to find something better than the Iran deal. All of this makes it fascinating, interesting, historic, but very much in its early stages.