Donald Trump's lawyer Rudy Giuliani says the North Korean leader begged on "his hands and knees" to reinstate their high-stakes summit in Singapore.

Mr Giuliani told a business conference in the Israeli city of Tel Aviv that Mr Trump's tough line forced Kim Jong-un to soften his stance.

He said there was no choice but to cancel the June 12 summit after Mr Kim insulted the US Vice President and threatened nuclear war.

"We said, 'Well, we're not going to have a summit under those circumstances,'" he said.

"Well, Kim Jong-un got back on his hands and knees and begged for it, which is exactly the position you want to put him in."

The historic summit, to be held at the luxurious Capella Hotel on Sentosa, was called back on just a week after Mr Trump sent a letter to Mr Kim saying he was pulling out of the talks.

In the letter, Mr Trump wrote he felt it was "inappropriate, at this time, to have this long-planned meeting" after "tremendous anger and open hostility" displayed in North Korea's statement calling US Vice President Mike Pence a "political dummy".

Mr Trump called the meeting back on after a successful meeting with Kim Yong-chol, a senior envoy from Pyongyang, who also delivered a letter from the North Korean leader.

After the meeting, Mr Trump said Kim Jong-un was committed to denuclearisation, and that the letter was "a very nice letter, a very interesting letter".

Kim Yong-chol presented Donald Trump with a "very interesting letter" from North Korean leader Kim Jung-un. ( Supplied: White House/Shealah Craighead )

During the same address in Tel Aviv, Mr Giuliani suggested similar tactics should be used with the Palestinian Authority, which has cut off ties with the US to protest Mr Trump's decision to recognise contested Jerusalem as Israel's capital.

"They have to be seeking peace. You have got to change the dynamic and put the pressure on them," Mr Giuliani said.

Mr Giuliani has become a lightning rod during his tenure on Mr Trump's team, drawing the President's ire for a series of scattershot interviews.

AP/ABC