Trump paired his Friday ultimatum with a social media post saying the US had "totally obliterated" military targets on the island, the export terminal for 90 per cent of Iran's oil shipments, which lies about 500km northwest of the strait.
US strikes did not target Kharg's oil infrastructure, but "should Iran, or anyone else, do anything to interfere with the Free and Safe Passage of Ships through the Strait of Hormuz, I will immediately reconsider this decision", Trump wrote.
Iran could not defend against US attacks and "would be wise to lay down their arms, and save what's left of their country", the president posted on his Truth Social platform.
Iran, however, showed no sign of capitulating or bowing to US-Israeli military pressure.
Iran's armed forces responded to the Kharg attack by saying any strike on their country's oil and energy infrastructure would lead to strikes on facilities owned by oil companies co-operating with the United States in the region, Iranian media reported.
Iran's semi-official Fars news agency reported, citing sources, that more than 15 explosions were heard on the island during the US attacks.
The sources said air defences, a naval base and airport facilities were hit, but there was no damage to oil infrastructure.
Markets were watching for any sign that US strikes had damaged the island's network of pipelines, terminals and storage tanks, with even minor disruptions able to further tighten global supply and add pressure to a volatile market.
Iran also claimed success in shooting down five drones over its airspace, bringing to 114 the total US and Israeli drones it had downed during the war, Iranian state TV reported on Saturday.
Oil prices have swung sharply on Trump's changing comments about the likely duration of the war, which began on February 28 with massive US and Israeli bombardments of Iran and quickly spread into a regional conflict with broad consequences for worldwide energy and stock markets.
The US embassy in the Iraqi capital Baghdad was hit in a missile attack on Saturday, Iraqi security sources said.
In other attacks across the region, Iran's Revolutionary Guards said they had carried out strikes on Israel with Lebanon's Hezbollah militia, Iran's Tasnim news agency reported.
On Friday, the Israeli military said its air force had struck more than 200 targets in western and central Iran, including ballistic missile launchers, air-defence systems and weapons production sites.
After two weeks of war, 2000 people have been killed, most in Iran but many in Lebanon and a growing number in the Gulf.
US forces have suffered casualties, including the deaths of all six crew members aboard a refuelling aircraft that crashed in western Iraq.
As well as Iran's missile and drone attacks on Israel and Gulf state allies of the US, Iran's Islamic Revolutionary Guard Corps has sought to disrupt shipping through the Strait of Hormuz, a conduit for 20 per cent of the world's fossil energy supplies.
Trump told reporters on Friday the US Navy would soon start escorting tankers through the waterway.
Although he has previously said the war would last only weeks, Trump on Friday declined to publicly project an end date for the conflict, telling reporters: "It'll be as long as it's necessary."
Iran continued to export crude oil while other producers in the Gulf halted their shipments for fear of Iranian attacks.
Iran's new supreme leader, Mojtaba Khamenei, in his first public comments, vowed to keep the Strait of Hormuz shut and urged neighbouring countries to close US bases on their territory or risk being attacked themselves.
US Defense Secretary Pete Hegseth said on Friday Iran's new leader was wounded and likely disfigured, questioning Khamenei's ability to govern.
No images have been released of Khamenei since an Israeli strike at the start of the war that killed much of his family, including his father and wife.
Iran says the new supreme leader was wounded, but is not "impaired".
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