Anticipation of a declaration to end the war is building after Pompeo made the remarks about the timing of the meeting on Wednesday, saying: “It may happen in October, but more likely sometime after that.”

“We’re working diligently to make sure we get the conditions right so that we can accomplish as much as possible during the summit. But we hope it will be soon,” Pompeo said, adding that he was already preparing to set up the next summit.

Moon Jae-in makes first ever public speech by South Korean leader in North

Also on Wednesday, Pompeo met with North Korean counterpart Ri Yong-ho in New York to discuss arrangements for both the meeting and the denuclearisation of the Korean peninsula, and accepted an invitation to visit Pyongyang for further discussions.

Alongside photos of their meeting, Pompeo tweeted on Wednesday morning that the talk had been “very positive” and that “Much work remains but we will continue to move forward.”

At the UN on Wednesday morning, Trump told reporters that the timing and location of his next summit with Kim would be announced in the “very near future”.

When asked what North Korea had to do before his next meeting with Kim, Trump said the two had made “a tremendous amount of progress” since last year. “They’re denuclearising North Korea. We have a wonderful relationship going between our country and them,” he said.

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South Korean President Moon Jae-in on Tuesday also announced that the two Koreas and the US had “generally formed a consensus” on the issue, fuelling expectations for an inter-Korean reconciliation.

Moon and Pompeo’s remarks came after the two Koreas agreed during a summit last week that the North would permanently dismantle nuclear facilities in Yongbyon if the US takes corresponding measures – a move that Moon said would be a conciliatory gesture conducive to ending hostile relations and speeding up efforts to end the war.

The talks between Trump and Kim would aim to reach agreement on specific denuclearisation steps before moving on to the declaration, observers said. These steps would be essential if international sanctions against Pyongyang are to be lifted, and to open up the economic development opportunities the North is seeking.

The Korean war ended in 1953 after an armistice was signed – by China, the United Nations Command and North Korea – but no formal peace agreement was ever reached.

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Chin Young, a South Korean lawmaker with the ruling Democratic Party of Korea, said it was in Seoul’s interests for the summit to be held soon.

“If the conditions are right, Seoul would want to see the second Trump-Kim summit as early as possible,” Chin said.

“It is in our best interests to pursue an early denuclearisation, and thus further improve inter-Korean relations,” Chin said, suggesting that the North needed to denuclearise before major economic projects between the two Koreas could go ahead.

A South Korean parliament source also anticipated that the declaration ending the war could be made during Kim’s planned visit to Seoul later this year, possibly in November.

While the US will have different political motivations for the Trump-Kim summit, holding it sooner would also serve Washington’s interests, according to observers.

A summit held before the US midterm elections in November “may be a way for President Trump to score more political points with his key Republican voter base”, said James Floyd Downes, a lecturer in comparative politics at Chinese University of Hong Kong.

“If Trump delivers on the summit, this is likely to go down well with his voter base. However, at the same time, it is also difficult to predict whether such a summit taking place would have an overall positive effect,” he added.

The Chinese view on the second Trump-Kim summit is complicated, in that Beijing is supportive of the talks but would not want to see Washington gaining more influence in the region, especially as China and the US remain locked in a trade war, analysts say. Trump has hardened his rhetoric against China, saying Beijing is not enthusiastic about denuclearisation.

China would also want to be part of further talks on the end-of-war declaration.

“It is of paramount importance that China should be involved in the [peace treaty] process … If China is not involved in the process, this will most likely create further polarisation between the United States and China, potentially exacerbating the chances of a full peace treaty negotiation being reached,” Downes said.

Cheng Xiaohe, an associate professor of international relations at Renmin University in Beijing, also said it was important for China to keep a seat at the table for peace talks.

“Whether China agrees or not, the second Trump-Kim summit will take place. So it would be wise for China to continue its engagement and be supportive of the peace process,” he said.

Zhao Tong, a fellow at Carnegie’s Nuclear Policy Programme at the Carnegie-Tsinghua Centre for Global Policy in Beijing, said China was generally supportive of the summit as it could help to stabilise the situation on the Korean peninsula.

“[But Beijing] will make sure it is formally involved in the peace treaty negotiation. China thinks it is an important stakeholder in this process and cannot be excluded,” Zhao said.

Additional reporting by Zhenhua Lu