"Today Iran will be hit very hard! Under serious consideration for complete destruction and certain death, because of Iran's bad behaviour, are areas and groups of people that were not considered for targeting up until this moment in time," Trump said in a post on Truth Social on Saturday, as the war enters its second week.
He also noted that Iran had apologised to its neighbours for its strikes against them, a move he cast as a surrender.
Iranian President Masoud Pezeshkian's had apologised in an apparent bid to ease regional anger at Tehran's strikes on Gulf Arab civilian targets.
The US-Israeli war on Iran has already spilled beyond Iran's borders, as Tehran has responded by hitting Israel and Gulf Arab states hosting US military installations and Israel has attacked Lebanon's Iran-backed Hezbollah armed group.
The UAE, Kuwait, Qatar, Bahrain and Saudi Arabia have reported drone and missile attacks in the past week.
Pezeshkian said Iran's temporary leadership council had approved suspending attacks on nearby countries - unless an attack on Iran came from those nations.
"I personally apologise to neighbouring countries that were affected by Iran's actions," he said on Saturday.
How far Pezeshkian's statement reflects a decision to back off by Iran, or why, is not yet clear, with some strikes still reportedly directed at Gulf states on Saturday morning.
Iran had mended fences with its Gulf neighbours in recent years - a diplomatic campaign that imploded as the Revolutionary Guards launched a blitz of drones and missiles in the past week.
Gulf states voiced immediate outrage that their civilian infrastructure - hotels, ports and oil facilities - were struck despite their having had no part in the US-Israeli attacks.
While Gulf states host US military bases, they had told Washington they would not allow these to be used for any attacks on Iran.
Iran's apparent strategy of maximum chaos has driven up the costs of the conflict by raising energy prices, hurting global business and logistics links and shaking trust in the stability of a critical region for the world's economy.
Pezeshkian's remarks came as diplomatic prospects for an end to hostilities appeared bleak, with US President Donald Trump on Friday demanding Tehran's "unconditional surrender".
The US-Israeli attacks have killed at least 1332 Iranian civilians and wounded thousands, according to Iran's UN ambassador, Amir Saeid Iravani.
Iranian attacks have killed 11 people in Israel, and at least six US service members have been killed.
Early on Saturday, the Iranian army said its navy had carried out drone strikes against targets in Israel as well as US gathering points and bases in Abu Dhabi and Kuwait, in an apparent response to the US attack on its ship IRIS Dena that killed dozens of sailors.
The Islamic Revolutionary Guard Corps said it struck three positions of separatist groups in Iraq's Kurdistan region, and warned that if separatist groups took any action against Iran's territorial integrity, "we will crush them".
The Israeli military earlier said it had identified missiles launched from Iran towards Israel.
Shortly after the barrage, the Israeli army said it had begun a wave of strikes targeting infrastructure in Tehran.
Israel also attacked neighbouring Lebanon, where it said it was hitting Iranian and Hezbollah targets.
The war has roiled global markets and oil prices have hit multi-year highs with the Strait of Hormuz effectively shut.
About one-fifth of global oil moves daily through the strait.
Iran has described the conflict as an unprovoked attack and the killing of supreme leader Ayatollah Ali Khamenei as an assassination.
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