President Donald Trump told the United Nations on Tuesday he was deciding whether to "annihilate" Iran -- before revealing that US and Iranian officials had held talks for the first time in months.

Trump's carrot-and-stick approach came as he delivered a bombastic speech to the UN General Assembly in New York focused heavily on his stalled, unpopular war against the Islamic Republic.

"I have a big decision to make -- will a deal be made with Iran that lets them rebuild and create a far greater country?" the 80-year-old said in his speech, during which all but one member of the Iranian delegation walked out.

"Or do I annihilate the Islamic Republic and do it quickly, never giving them a chance to kill and destroy people and countries again? Do I drive them into hell with no chance of survival?"

Trump said he believed Iran would make a deal immediately after November's midterm elections -- in which Republicans face losing control of Congress due largely to the conflict's drag on the US economy.

But just hours later, Trump revealed that Iranian and US representatives had met for "very good" talks on the sidelines of the UN gathering.

The meeting lasted three hours and included Trump's business friend-turned roving global negotiator Steve Witkoff and son-in-law Jared Kushner, he said.

"They had a very good meeting, a very productive meeting -- they have another one scheduled in the very near future," Trump told reporters as he met Ukrainian President Volodymyr Zelensky.

"I can't imagine why they wouldn't want to do it. It's potential greatness, or obliteration."

Witkoff told reporters that "I feel very good right now" about the Iranian meeting but would not give further details.

It is believed to be the first face-to-face meeting between Iranian and US officials since US Vice President JD Vance met senior Tehran officials in Switzerland in June.

Ukraine talks

Trump promised when the US and Israel launched the war on February 28 that it would be over in four or five weeks, but the conflict is now grinding on well into its sixth month.

A ceasefire agreed in April broke down within weeks and negotiations have since stalled, with Iran refusing to cede control over the Strait of Hormuz shipping lane.

Trump has sought to justify the economic pain of high fuel prices caused by the war amid mounting voting anger, saying that Iran cannot be allowed to develop a nuclear weapon.

Despite the belligerent tone of much of his speech, Trump portrayed himself as a peacemaker who was acting in America's interests, declaring: "While others have ignored threats, I have confronted them."

Yet Trump's meeting with Zelensky underscored that he is still yet to secure a deal to end Russia's invasion of Ukraine, a war that he once claimed he could settle in 24 hours.

Trump insisted he was working with both sides to end the war, despite little evidence of Russian President Vladimir Putin being open to any settlement.

"We're working very closely with the leaders of Russia and Ukraine, and we will get that one done. It's going to happen, I think, more quickly than people understand," Trump said in his UN speech.

While at the UN, Trump also signed a security deal with Greenland and Denmark which has -- for now at least -- cooled his calls for seizing the autonomous Danish territory.

The pact will see the United States build two military bases in southern and eastern Greenland and bars non-NATO powers from establishing any military presence on the arctic island.

"It's going to be a long-term, fantastic relationship," said Trump, whose territorial claims to Greenland since his return to power have deeply alarmed traditional US allies.