Donald Trump's administration asked Japan's prime minister Shinzo Abe to nominate him for a Nobel Peace Prize after he and North Korean dictator Kim Jong-un met for a historic summit, according to a Japanese newspaper.

On Friday (US time), Trump boasted during a White House Rose Garden press event that Abe had handed him "the most beautiful copy" of a five-page letter about the nomination but concluded "I'll probably never get it", the Daily Mail reported.

The request came months after the Trump-Kim summit in Singapore on June 12, according to the newspaper Asahi Shimbun.

Abe ultimately submitted Trump's name, citing his efforts to defuse decades-long tensions on the Korean peninsula.

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"He said, 'I have nominated you, respectfully, on behalf of Japan. I am asking them to give you the Nobel Peace Prize'," Trump told reporters. "I said 'thank you'.

"Many other people feel that way, too. I'll probably never get it. That's okay,' he said.

Abe and his chief spokesman declined to say if the PM nominated the US President for the prize.

Abe noted while speaking in Parliament on Monday (Japan time) that the Nobel committee does not disclose the parties behind nominations for a half-century. He said, "I thus decline comment."

The government's top spokesman, Yoshihide Suga, told reporters that Japan highly valued Trump's efforts on North Korea's nuclear disarmament, but he echoed Abe in refusing other comment.

The Japanese newspaper Asahi Shimbun reported on Sunday, citing unnamed government sources, that Abe nominated Trump's at the president's request.

It's unclear how common it is for governments to lobby each others' leaders for award endorsements.

The Japanese Embassy in Washington did not respond to a request for comment on Sunday. The White House did not immediately respond to a request for comment.

Trump has made strides in opening talks with North Korea, saying consistently that the hermit kingdom's belligerence should have been countered by his predecessors.

Last year's meeting was the first between a sitting American president and a North Korean head of state.

A spokesman for Japan's Foreign Ministry in Tokyo told Reuters that it was aware of Trump's remarks but "would refrain from commenting on the interaction between the two leaders".

The Nobel Foundation's website says a nomination for the Nobel Peace Prize may be submitted by any person who meets the nomination criteria, which includes current heads of states.

The former non-voting secretary of the Nobel Peace Prize committee said in 2015 that members regretted giving the prestigious award to former president Barack Obama in 2009, less than a year into his first term.

Geir Lundestad told the Associated Press that the committee had hoped the prize would strengthen Obama, but instead it was met with ridicule since he hadn't yet had a significant impact on global affairs.

"No Nobel Peace Prize ever elicited more attention than the 2009 prize to Barack Obama," Lundestad wrote in his memoir.

"Even many of Obama's supporters believed that the prize was a mistake. In that sense the committee didn't achieve what it had hoped for."

Trump noted on Friday that "they gave it to Obama".

"He didn't even know what he got it for. He was there for about 15 seconds and he got the Nobel Prize. He said, 'Oh, what did I get it for?'"

The anecdote came as he hailed Pyongyang's "tremendous" economic potential and his "great relationship" with Kim ahead of a second scheduled summit between the two leaders late next week.

Trump also took a second dig at Barack Obama, suggesting his predecessor had been close to going to war with the nuclear-armed state.

Recalling a conversation he had with Obama shortly before his inauguration, Trump said: "I don't want to speak for him but I believe he would have gone to war with North Korea.

"I think he was ready to go to war, he told me he was so close to starting a big war with North Korea. Where are we now? No missiles, no rockets, no nuclear testing.

"We've learned a lot. But much more importantly than all of it – much more important, much, much more important than that – is we have a great relationship. I have a very good relationship with Kim Jong-un. And I've done a job."