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President Trump and North Korean leader Kim Jong Un meet at the Korean Demilitarized Zone in Panmunjom, South Korea, on June 30, 2019. Reuters

The three-part series, titled "Trump Takes On the World," discloses new details about how Trump and Kim negotiated North Korea's nuclear program, which eventually ended without a deal.

Trump, who had left the meeting abruptly, told the press at the time: "Sometimes you just have to walk."

But the former president didn't leave without making an unusual offer first.

"President Trump offered Kim a lift home on Air Force One," Matthew Pottinger, the top Asia expert on Trump's National Security Council, told the BBC.

"The president knew that Kim had arrived on a multi-day train ride through China into Hanoi and the president said: 'I can get you home in two hours if you want.' It was a gracious gesture," he added.

Kim declined the offer, according to Pottinger.

Trump is seen boarding Air Force One alone after Kim declined his offer for a ride home

Pottinger said the 'gracious gesture' astounded him and other officials who witnessed it, but it wasn't the only puzzling exchange between Trump and Kim.

Former National Security Adviser John Bolton also appeared in the docu-series and spoke of the 'bromance' the leaders formed following their first meeting in Singapore in June 2018.

'Trump thought he had a new best friend,' Bolton said.

He described another troubling instance when Trump informed his team that he had agreed to Kim's request to cancel joint military exercises between the US and South Korea.

'Kim Jong-un, as he had many times in the past, complained about the big joint exercises between South Korea and American forces, which had been going on on the Korean peninsula for about 60 years plus,' Bolton said.

'Trump, out of nowhere, said: "I'm going to cancel the war games [as he called them]. There's no need for them, they're expensive and it will make you happy."

'I couldn't believe it. [Secretary of State Mike] Pompeo, [Chief of Staff John] Kelly and I were sitting there in the room with Trump and we weren't consulted.

'It came simply from Trump's own mind. It was an unforced error; it was a concession for which we got nothing in return.'

The docu-series also offered new details about how Trump and Kim's first meeting in 2018 was arranged. At the time, Trump's willingness to sit down with Kim came as a surprise to many, after the president had threatened to unleash 'fire and fury' on North Korea while deriding Kim as 'Rocket Man'.

Trump and Kim are pictured together during the summit in Hanoi on February 28, 2019

Jeff Feltman, the United Nation's Under-Secretary General for Political Affairs, revealed to BBC that he delivered a 'secret message' to Kim with Trump's offer of a meeting.

Feltman explained that the North Korean government invited him to visit Pyongyang, and the US State Department initially didn't think he should accept.

A few weeks later, UN Secretary General Antonio Guterres visited the White House to discuss the invitation, Feltman said.

'[Trump and Guterres] were comparing notes on what was happening, what might be possible, how dangerous was it, how likely would a military response be, all that sort of thing,' Feltman said.

'Secretary General Guterres said to President Trump: "Jeff Feltman has this strange invitation to go to Pyongyang and lead a policy dialogue with the North Koreans."

'And Trump leaned over toward him and said: "Jeff Feltman should go to Pyongyang and Jeff Feltman should tell the North Koreans I'm willing to sit down with Kim Jong-Un."'

Feltman then traveled to Pyongyang and relayed Trump's offer to North Korea's foreign minister, he said.

'There was a bit of silence before the foreign minister said: "I don't believe you, why should I believe you,'" he recalled.

'And I said: "Look, I'm not asking you to believe me. What I'm telling you is that the UN was entrusted with a message from President Trump; I am the carrier of that message."'

'Trump thought he had a new best friend,' Bolton said of Trump's first meeting with Kim in Singapore in June 2018 (pictured)

Feltman added: 'I went to Pyongyang deeply, deeply concerned given this feeling that war was imminent. I left Pyongyang terrified that what we really risked was an accidental war.'

Several months passed without a response from Kim, before the dictator informed South Korea that he wanted to meet with Trump.

Trump's national security adviser at the time, HR McMaster, said he was shocked when his South Korean counterpart, Chung Eui-yong, presented the news at the White House.

'Ambassador Chung just about fell out of his chair because he thought it was going to be kind of a hard sell,' McMaster told BBC.

McMaster said he expressed 'serious reservations' about the meeting, but Trump went ahead and accepted anyway.

'I felt that it would be better to let Kim Jong-un feel the pressure a little bit longer,' he said. 'But, of course the president wouldn't resist the opportunity.'

"Trump Takes on the World," directed by Tim Stirzaker, will be broadcast on BBC2 on Wednesday.

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