Trump's warning came at the end of a day that saw global financial markets seesawing on concerns that Iran's security establishment was rallying behind new Supreme Leader Mojtaba Khamenei and was not prepared to back down any time soon.
Trump said the US had inflicted serious damage on Iran's air force and navy and predicted the conflict would end well before the initial four-week time frame he had laid out, though he has not defined what victory would look like.
He warned that US attacks could rise sharply if Iran sought to block tanker traffic through the Strait of Hormuz, which handles one-fifth of the world's oil supply.
"We will hit them so hard that it will not be possible for them or anybody else helping them to ever recover that section of the world," Trump said at a news conference on Monday night.
In response, Iran's Revolutionary Guards said it would not allow "one litre of oil" to leave the region if attacks from the US and Israel continued.
"We are the ones who will determine the end of the war," a spokesperson said, according to state media.
The conflicting signals sent markets on a rollercoaster, with oil prices surging and stock markets nosediving before swinging in the other direction after Trump's prediction of a quick end to the war and reports of a possible ease in sanctions on Russian energy.
Khamenei, 56, a Shi'ite cleric with a power base among the security forces and their vast business empire, has been declared unacceptable by Trump, who has demanded Iran's unconditional surrender.
Iranian state media showed large crowds in several cities rallying behind the new leader, waving Iranian flags and holding portraits of his father Ali Khamenei, the supreme leader killed by an Israeli strike on the war's first day.
In Isfahan, state TV reported the sound of nearby explosions from apparent airstrikes as loyalists gathered in the historic Imam Square, chanting "God is the Greatest" below a stage with portraits of Ali and Mojtaba Khamenei.
Many Iranians had initially celebrated the elder Khamenei's death, weeks after his security forces killed thousands of anti-government protesters in the worst domestic unrest since the era of Iran's 1979 revolution. But there has since been little sign of anti-government activity.
Israel says its war aim is to overthrow Iran's system of clerical rule.
US officials mainly say Washington's aim is to destroy Iran's missile capabilities and nuclear program, but Trump has said the war can end only with a compliant Iranian government.
Israel had said it would kill whoever succeeded the elder Khamenei unless Iran ended its hostile policies.
The war has effectively shut the Strait of Hormuz, a chokepoint for global oil and liquefied natural gas transport, leaving tankers unable to sail for more than a week and forcing producers to halt pumping as storage fills.
Brent crude futures jumped about seven per cent to settle at their highest price since 2022 after soaring by as much as 29 per cent during the session, as Saudi Arabia and other OPEC members cut supplies. But prices fell in post-settlement trade.
The price of gasoline has particular political resonance in the US, where voters cite rising costs as a top concern ahead of the November midterm elections.
After speaking with Russian President Vladimir Putin, Trump said the US would waive oil-related sanctions on "some countries" to ease the shortage.
According to multiple sources, that could mean a further easing of sanctions on Russian oil, which could complicate efforts to punish Moscow for its war in Ukraine. Other options include a possible release of oil from strategic reserves or restricting US exports.
Tehran was choked in black smoke after an oil refinery was hit, an escalation in strikes on Iran's domestic energy supplies. World Health Organization chief Tedros Ghebreyesus warned the fire risks contaminating food, water and air.
Turkey said NATO air defences had shot down a ballistic missile that was fired from Iran and entered Turkish airspace, the second such incident of the war.
Israel's military said it had launched new attacks in central Iran and struck the Lebanese capital Beirut, where Israel has extended its campaign after the Iran-backed militia Hezbollah fired across the border.
US-Israeli attacks have killed at least 1332 Iranian civilians and wounded thousands, according to Iran's UN ambassador. Lebanon has reported more than 400 people killed there, with nearly 700,000 people fleeing their homes.
In Israel, ambulance workers said one man died from shrapnel wounds at a construction site near Tel Aviv's international airport, raising to 11 the death toll from Iranian strikes.
with AP
