"President Trump didn't take that. What he did was he called off the summit," he said.

Giuliani said Kim quickly changed his position, expressed willingness to discuss denuclearisation and asked to have the meeting again.

"That's what I mean by begging for it," Giuliani said.

The summit is back on in Singapore next Tuesday.

Giuliani, Trump's lawyer in the Russian investigation, noted that he was sharing a personal opinion and was not part of the US foreign policy team.

The former United States Attorney for the Southern District of New York and strong supporter of Israel, was in Israel for a number of appearances, including a speech to a Tel Aviv business conference earlier in the day and an address late on Wednesday to OneFamily, a group that supports Israeli families whose loved ones have been wounded or killed in Palestinian attacks.

Speaking earlier in the day, Giuliani also suggested high-pressure tactics should be used with the Palestinian Authority, which has cut off ties with the US to protest Trump's decision to recognise contested Jerusalem as Israel's capital.

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

Giuliani is leading the defence of Trump in special counsel Robert Mueller's Russia interference investigation.

Trump's team and allies have waged a public relations campaign against Mueller and the Justice Department to discredit the investigation and soften the impact of potential findings. In the latest salvo, Giuliani accused Mueller of trying to "frame" the President.

"They don't have a crime. And that's why I say they're trying to frame him. Because if they had any sense, they would realize they're trying to put together a case on an innocent man. And that's what we call in America framing somebody," Giuliani said.

Though Trump insists he did nothing wrong, the statements from him and his lawyers have made clear that much of their defence revolves around establishing that he was constitutionally empowered to take the actions he took.

Giuliani rejected criticism that the defence team was attacking the justice system or public institutions.

"We're trying to purify institutions," he added, accusing the media of trying to convict Trump and saying the prosecutors are "not saints" immune from attack.

Nonetheless, Giuliani said he remains in touch with Mueller, and that there have been discussions about allowing investigators to question the President. But he said his client needs assurances he won't be railroaded.

"The President would very much like to do an interview. His lawyers are very, very suspicious," he said. "They're going to have to convince us that it's going to be a fair interview."

He said so far, Mueller has not produced evidence indicating wrongdoing by the President.

"If they can show us some hard, incriminating facts from that evidence, then we would consider advising our client to be interviewed," he said.