Trump set a Monday deadline of 7.45pm EDT (10.45am on Tuesday AEDT), warning late on Saturday that the United States would strike Iran's power plants unless Tehran fully reopened the Strait of Hormuz within 48 hours.
The prospect of tit-for-tat strikes on civilian infrastructure further unsettled oil markets, with prices opening choppy in Asia trading.
After more than three weeks of heavy US and Israeli bombardment that officials say has sharply reduced Iran's missile capabilities, Tehran has continued to demonstrate its ability to strike back.
Air raid sirens sounded across parts of northern and central Israel, including in Tel Aviv, and the occupied West Bank overnight on Sunday, warning of incoming missiles from Iran.
The Israeli military said early Monday it had begun a wide-scale wave of strikes targeting Iranian infrastructure in Tehran.
Iranian news agencies said at least one child was killed and several people were injured in the bombing of a residential area in western Khorramabad city.
A residential neighbourhood in the northwestern city of Urmia was damaged by an air strike, Iranian news agencies reported.
There were no immediate reports of casualties.
Trump's warning came less than a day after he signalled the United States might be considering winding down the conflict, even as US Marines and heavy landing craft were heading to the region.
"If Iran's fuel and energy infrastructure is attacked by the enemy, all energy infrastructure, as well as information technology ... and water desalination facilities, belonging to the US and the regime in the region will be targeted pursuant to previous warnings," Iranian military spokesman Ebrahim Zolfaqari said.
While attacks on electricity could hurt Iran, they could be catastrophic for its Gulf neighbours, which consume about five times as much power per capita, in part by powering desalination plants that produce most of the water consumed there.
Iran's parliament speaker, Mohammad Baqer Qalibaf, doubled down, writing on X that critical infrastructure and energy facilities in the Middle East could be "irreversibly destroyed" should Iranian power plants be attacked.
Iran's powerful Revolutionary Guards said it would also mean the shipping lane where a fifth of global oil and liquefied natural gas usually transits along Iran's southern coast would remain shut.
"The Strait of Hormuz will be completely closed and will not be opened until our destroyed power plants are rebuilt," the Guards said in a statement.
The Saudi defence ministry said early on Monday that two ballistic missiles had been launched towards Riyadh, with one missile intercepted while the other fell in an uninhabited area.
On Sunday, Iranian strikes on two southern Israeli towns injured dozens in what an Israeli hospital described as a major casualty event.
The towns were close to Israel's secretive nuclear reactor and a number of military installations, including Nevatim Air Base, one of the country's largest.
More than 2000 people have been killed during the war the US and Israel launched on February 28, which has upended markets, spiked fuel costs, fuelled global inflation fears and convulsed the postwar Western alliance.
Iranian attacks have effectively closed the Strait of Hormuz, causing the worst oil crisis since the 1970s.
"If Iran doesn't FULLY OPEN, WITHOUT THREAT, the Strait of Hormuz, within 48 HOURS from this exact point in time, the United States of America will hit and obliterate their various POWER PLANTS, STARTING WITH THE BIGGEST ONE FIRST!" Trump posted on social media on Saturday night.
Iranian media quoted the country's representative to the International Maritime Organisation as saying the strait remained open to all shipping except vessels linked to "Iran's enemies".
