Speaking to NBC News on Saturday, Trump said the US could hit the island "a few more times just for fun", adding that he was not ready to reach a deal with Tehran as conditions were "not good enough yet".
He also cast doubt on whether Iran's new Supreme Leader, Mojtaba Khamenei, was even alive.
"So far, nobody has been able to show him," Trump said.
The new Iranian leader has not been seen in public since taking office on 8 March.
Meanwhile, the US Central Command (Centcom) confirmed American forces had already struck more than 90 military targets on the island.
Iran's Foreign Minister Abbas Araghchi warned that if Iranian energy facilities were attacked, Tehran would target US companies in the region.
The Islamic Revolutionary Guard Corps called on American businesses to leave the Middle East entirely.
Iran also widened its threats, with the head of Iran's national security commission declaring Ukraine a "legitimate target," accusing Kyiv of supplying drones to Israel.
Ukraine dismissed the warning as "absurd".
President Volodymyr Zelensky pointed out that it was Russia which had supplied Iran with Shahed drones, later used against US bases in the region.
The broader conflict continues to escalate.
Lebanese authorities say 826 people, including 100 children, have been killed and over 816,000 displaced since Israel launched operations against the Iranian-backed group Hezbollah on 2 March.
A drone strike on an air base in Kuwait, also hosting US military personnel, wounded three soldiers.
Saudi Arabia, the UAE, Qatar and Dubai all reported intercepting Iranian drones overnight.
Formula 1 has cancelled the Bahrain and Saudi Arabian Grands Prix, originally scheduled for April, citing the situation in the region.
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Source: PAP