Trump said in a post on Truth Social that the US and Iran have had "VERY GOOD AND PRODUCTIVE" conversations with Iran over the past two days about a "COMPLETE AND TOTAL RESOLUTION OF HOSTILITIES IN THE MIDDLE EAST".
In his message, written entirely in capital letters on Monday, he said he had instructed the defence department to postpone the strikes pending the outcome of current talks.
On Saturday, Trump had warned that Iranian power plants would be destroyed if Tehran failed to "fully open" the Strait of Hormuz to all shipping within 48 hours.
Trump set a deadline of 7.44pm EDT on Monday (10.44am on Tuesday AEDT).
His comments sparked threats of retaliation from Iran's Revolutionary Guards, who said they would attack Israel's power plants and those supplying US bases across the Gulf region if Trump followed through with his threat to "obliterate" Iran's power network.
Iran's Defence Council escalated its threatened retaliation on Monday, saying Tehran would cut all Gulf routes by laying sea mines if Trump followed through, state media reported.
More than 2000 people have been killed in the war the US and Israel launched on February 28, which has upended markets, driven up fuel costs, fuelled global inflation fears and convulsed the postwar Western alliance.
The threat of strikes on Gulf electricity grids raised fears of mass disruption to desalination for drinking water, and further rattled oil markets.
Iranian attacks have effectively closed the Strait of Hormuz, which carries a fifth of global oil and liquefied natural gas.
Fatih Birol, executive director of the International Energy Agency, said the resulting energy crisis was worse than the two oil shocks of the 1970s and the gas shortage connected to Russia's 2022 invasion of Ukraine put together.
Iranian media on Sunday 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".
Indian and Pakistani vessels are among those that have reportedly been allowed safe passage.
More than 2000 people have been killed in the war the US and Israel launched on February 28, which has upended markets, driven up fuel costs, fuelled global inflation fears and convulsed the postwar Western alliance.
The threat of strikes on Gulf electricity grids on Sunday raised fears of mass disruption to desalination for drinking water, and further unsettled oil markets, with prices opening choppy in Asian 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 on Monday it had begun its latest broad wave of strikes on infrastructure in Tehran.
The Washington Post reported that Iranian Supreme Leader Mojtaba Khamenei was "injured, isolated, and not responding to messages directed to him".
An Iranian official said earlier in March that Khamenei was lightly injured.
Khamenei succeeded his father Ayatollah Ali Khamenei, who was killed in the first wave of strikes on February 28, but has not been seen in public since his appointment.
Iranian news agencies said six people had been killed and 43 injured in strikes on residential buildings in the western city of Khorramabad.
Across the Gulf, the Saudi defence ministry said two ballistic missiles had been launched towards Riyadh.
One was intercepted while the other fell in an uninhabited area.
