US President Donald Trump has used his speech to the United Nations General Assembly to defend his "America First" policies of putting US interests ahead of any move towards globalism, a message that was greeted by silence, blank stares, headshakes and even laughter at times from wary world leaders.

Key points: Trump defends economic record using political rally rhetoric

Trump defends economic record using political rally rhetoric UN delegates greet remarks with a combination of silence, headshakes and laughs

UN delegates greet remarks with a combination of silence, headshakes and laughs Iran threatened with more sanctions

Iran threatened with more sanctions China attacked on trade policy but no mentions made of Russia or Syria

Mr Trump said he honoured the right of every nation to pursue its own customs, beliefs and traditions and said the United States would never tell other nations how to live, work or worship.

He added the United States expected other nations to "honour America's sovereignty in return".

Mr Trump, who begins his political rallies with boasts about his economic record, used the same rhetoric before the crowd of world leaders and diplomats, telling them he had accomplished more than almost any previous US president.

"In less than two years, my administration has accomplished more than almost any administration in the history of our country," he said.

The remark led to some murmuring and laughter in the crowd, taking the President slightly aback. "So true," he said, looking directly into the audience.

"I didn't expect that reaction, but that's okay," he said, which was followed by more laughter and applause.

Mr Trump has long claimed that his predecessor's weak leadership prompted other nations "to laugh" at the US. ( AP: Evan Vucci )

Rouhani suggests Trump has 'weakness of intellect'

But his 35-minute speech in the green-marbled UN hall, while relatively low-key, was also aimed squarely at Iran, which the United States accuses of harbouring nuclear ambitions and fomenting instability in the Middle East through its support for militant groups in Syria, Lebanon and Yemen.

He attacked Iran as a "corrupt dictatorship" that is plundering its people to pay for aggression abroad, and threatened more sanctions against Tehran.

"Iran's leaders sow chaos, death and destruction," Mr Trump told the annual gathering. "They do not respect their neighbours or borders or the sovereign rights of nations."

In his address to the UN assembly later in the day, Iranian President Hassan Rouhani hit back, suggesting his American counterpart suffers from a "weakness of intellect".

"Confronting multilateralism is not a sign of strength. Rather it is a symptom of the weakness of intellect — it betrays an inability in understanding a complex and interconnected world," he said.

Mr Rouhani sharply criticised Mr Trump's decision to withdraw from the 2015 international nuclear deal with Iran, which was negotiated under former US president Barack Obama.

He said he had "no need for a photo opportunity" with Mr Trump and suggested the US President's pull-back from global institutions was a character defect.

"What Iran says is clear: no war, no sanctions, no threats, no bullying; just acting according to the law and the fulfillment of obligations," Mr Rouhani said.

Mr Trump, who said on Tuesday morning he had given up hope for a meeting with Mr Rouhani while both were in New York, said he would keep up economic pressure on Tehran to try to force a change in its behaviour.

"Additional sanctions will resume November 5th and more will follow, and we are working with countries that import Iranian crude oil to cut their purchases substantially," Mr Trump said.

Sorry, this video has expired Mike Pompeo and John Bolton speak at Iran summit

Mr Trump's national security adviser, John Bolton, addressing a group called United Against a Nuclear Iran, called the 2015 accord "the worst diplomatic debacle in American history" and had a warning for "the mullahs in Tehran".

"If you cross us, our allies, or our partners; if you harm our citizens; if you continue to lie, cheat, and deceive, yes, there will indeed be hell to pay," he said.

In his UN speech, Mr Trump compared US relations with Iran to what he called improved ties with North Korean leader Kim Jong-un, who Mr Trump met in Singapore in June as part of a still-unfulfilled drive to get Pyongyang to give up its nuclear weapons.

Mr Trump also criticised China for its trade practices but made no mention of Russia's interference in Syria or meddling in the US election.

In his address last year to the UN, Mr Trump insulted Mr Kim as a "rocket man" bent on nuclear destruction. On Tuesday, Mr Trump praised Mr Kim for halting nuclear and missile tests, releasing Americans held prisoner and returning some remains of US soldiers killed in the 1950s Korean War.

The two leaders are trying to arrange a second summit and are exchanging private correspondence. Mr Trump has said sanctions on North Korea would remain for now.

Sorry, this video has expired US President's boasts draw laughter at UN

ABC/Wires