Former New York Mayor Rudy Giuliani on Wednesday boasted that US President Donald Trump's tough line had forced the North Korean leader to beg to re-schedule a high-profile summit after the president abruptly called off the meeting.

After the cancellation, "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," Giuliani told a business conference in the Israeli city of Tel Aviv.

In an interview later with The Associated Press, Giuliani rejected suggestions that such comments might sour the atmosphere ahead of next week's summit in Singapore, saying that the North Korean leader must understand that the United States is in a position of strength.

"It is pointing out that the president is the stronger figure," Giuliani told the AP. "And you're not going to have useful negotiations unless he accepts that."

Giuliani said Trump had no choice but to call off the meeting after the North Koreans insulted Vice President Mike Pence, National Security Adviser John Bolton and threatened "nuclear annihilation" of the U.S.

"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 denuclearization 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 U.S. foreign policy team.

The former New York mayor is 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.

Giuliani is leading the defence of Trump in special counsel Robert Mueller's investigation into whether Trump associates coordinated with Russia during the 2016 presidential election, and whether Trump took steps to shut down that investigation through actions, including the firing of FBI Director James Comey.

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 the special counsel's potential findings. In the latest salvo, Giuliani accused Mueller of trying to "frame" the president.

Giuliani claimed that Mueller has produced no evidence of wrongdoing by the president, and has stacked his team with partisan Democrats, including supporters of Hillary Clinton's presidential campaign.

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 is 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.

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

Jerusalem - 6 June 2018

1. Set-up shot of US President Donald Trump's lawyer Rudy Giuliani

2. SOUNDBITE (English) Rudy Giuliani, US President Donald Trump's lawyer:

“What I’m saying is that (North Korean leader) Kim Jong Un had someone say terrible things about (US) Vice President (Mike) Pence. Terrible things about (National Security Advisor) John Bolton. And then had someone threaten nuclear annihilation of the United States. (US) President (Donald) Trump didn’t take that. What he did was he called off the summit and he was widely criticised for it. And Kim Jong Un changed his position. He said he was going to do denuclearisation. Again, we don’t have the conditions yet but at least that's a big shift and asked to have the meeting again. And that’s what I mean by 'begging for it'.”

3. Close of Giuliani

4. SOUNDBITE (English) Rudy Giuliani, US President Donald Trump's lawyer:

"It is pointing out that the president is the stronger figure and you're not going to have useful negotiations unless he accepts that. And my words don't matter - I'm not involved in the negotiations. But my comments as a citizen are very important."

5. Cutaway of Giuliani with associates

6. SOUNDBITE (English) Rudy Giuliani, US President Donald Trump's lawyer:

"In order to try to develop evidence against him, they have brought a number of very questionable cases. The prosecution of Mr. (Paul) Manafort for things in 2005 that had nothing to do with President Trump. I can't imagine why...whether Mr. Manafort did something wrong or not - I cant judge. But I can say it has nothing to do with President Trump. And then these Russians that were indicted, who are never going to come to the United States, who play dirty tricks like dressing up as clowns. If that is Russian collusion, I don't know maybe it is. But, the real question is there's not a single link to anybody in America. So what's that about if it isn't trying to formulate a case on the president when there is no evidence for it. A judge recently said that this investigation is more like investigating a man than a crime. Because, 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 realise they're trying to put together a case on an innocent man and that's what we call in America 'framing somebody'."

7. Cutaway of Giuliani taking photos with associates

8. SOUNDBITE (English) Rudy Giuliani, US President Donald Trump's lawyer:

"We're trying to purify institutions. You're just part of that whole...media that wants to turn around and convict President Trump when he's done nothing wrong. And nobody wants to recognise that that's what these people are engaged in. Well it's my job to defend a client and if I have to take on an Attorney General or an independent council, by God, I'll take them on. I'm not the first lawyer to do that. When someone is unfairly prosecuting you, you have got to point that out loudly and clearly - this is an unfair investigation. It has no basis in fact. President Trump did not talk to, meet with, or have anything to do with Russians at any time during the 2016 election. That is a totally phoney charge. And over a year-and-a-half and 20 million dollars later they don't have a single piece of proof that he did. Now, if you aren't framing him, then stop the investigation, put out your report and let the chips fall where they may."

9 . Cutaway of Giuliani taking photos with associates

10. SOUNDBITE (English) Rudy Giuliani, US President Donald Trump's lawyer:

"If they can show us some hard incriminating facts from that evidence, then we would consider advising our client to be interviewed. But, if we don't see it, then we have to conclude that we're not dealing with a fair-minded group of people."

11. Giuliani with associates

12. SOUNDBITE (English) Rudy Giuliani, US President Donald Trump's lawyer:

"Not only did (Robert) Mueller bring in heavy Democratic partisans to conduct the investigation of a Republican, he's also using the FBI agents who conducted the totally unfair, totally biased, in the other direction, investigation of Hillary Clinton. They should have used new agents, not agents that have conducted probably one of the most flawed investigations in American history."

13. Giuliani getting on a bus