"I have a big decision to make," Trump said in a speech at the UN General Assembly in New York on Tuesday.
"Will a deal be made with Iran that lets them rebuild and create a far greater country than it ever was before? ... Or do I annihilate the Islamic Republic and do it quickly, never giving them a chance to kill and destroy people and countries again?"
Iran's Armed Forces dismissed Trump's comments at the UN as "propaganda", saying their response is "full readiness to inflict more severe, crushing, and unpredictable blows on the aggressors".
But away from the fiery rhetoric, discussions continued to try to end the nearly seven-month conflict that began with joint US-Israeli strikes and has since killed thousands, driven up oil prices and drawn in neighbouring countries.
Trump said that envoys Steve Witkoff and Jared Kushner "had a very productive meeting today with mediators of Iran".
"I think there's a lot of momentum for them to make a deal," he said.
Trump also met the leaders of Middle Eastern countries who are keen to restore shipping through the Strait of Hormuz, the conduit for a fifth of global oil and gas shipments before the war, but are wary of giving their longstanding rival Iran too much power.
Many also host huge US military bases that have come under repeated Iranian attack throughout the war.
"We think that the situation with Iran could end right after the (November 3) midterm elections, maybe before. I don't know. You never know," Trump said as he met the leaders.
The diplomatic manoeuvring comes as Trump faces pressure on multiple fronts - rising energy costs at home, a widening regional conflict abroad, and the midterms six weeks away that could reshape his political standing.
A senior Iranian official said Tehran could reopen the Strait of Hormuz within days if the US eased military pressure and lifted its blockade on Iranian ports.
The senior Iranian official told Reuters that Tehran had conveyed its latest proposal to Washington through mediators last week and could reopen the strait to Gulf shipping within seven days if its demands were met.
In a reminder of Iran's firm position so far, Parliament Speaker Mohammad Baqer Qalibaf, who headed Iran's negotiating team at previous talks, said Iran would never surrender: "Trump must understand that he cannot impose his power on the Iranian people and its armed forces."
On the table is a Qatari proposal for a common security framework involving Iran and the Arab Gulf states, regional sources said. One source said Iran was reviewing the proposal.
Saudi Arabia, the largest of the Gulf states, has been drawn deeper into the war as Iran-aligned Houthi fighters have advanced in Yemen, routing forces of the Saudi-backed government and threatening Saudi oil exports through the Red Sea.
The US, which bombed the Houthis for two months last year, has so far rebuffed repeated pleas from Saudi Arabia's Crown Prince Mohammed bin Salman to rejoin the fight.
Oil markets did find some relief on Tuesday after sources told Reuters that Saudi Arabia had restarted operations at its East-West Pipeline and could resume exports from the Red Sea port of Yanbu within hours, albeit at reduced volumes.
The pipeline, Saudi Arabia's main export route bypassing wartime disruption in the Strait of Hormuz, had been shut after attacks this month that Riyadh blamed on Iranian-backed groups in Iraq.
