Speaking during a NATO Summit appearance in Ankara, Turkey, Trump said the US had already carried out significant strikes overnight and was prepared to escalate further.
"We hit them very hard last night. Very, very hard. We'll probably hit them hard again tonight. I'll give them a little warning. We're going to hit them hard tonight," Trump said, as reported by several media.
Accusing Tehran of attacking ships with drones and missiles, he added, "They are behaving very badly."
'Iran can't have a nuclear weapon'
On the sidelines of the summit, Trump reiterated that the conflict was aimed at preventing Iran from acquiring nuclear weapons.
He claimed US officials had made progress in talks with Tehran but accused Iranian leaders of publicly denying the discussions after leaving the negotiating table.
"I think we've made a lot of progress... they'll agree on everything, and then they'll go have a news conference and say, 'We never even talked about it.'"
In unusually blunt remarks, Trump described Iran's leadership as "cuckoo."
"There's something wrong with these people, and for 47 years they've been the bully of the Middle East. They're not the bully anymore... All we want is very simple—they can't have a nuclear weapon."
Threat to target boats, infrastructure
Trump also suggested the US could intensify military operations by targeting additional Iranian vessels and critical infrastructure.
"We could knock out more boats tonight," he said, adding that electricity and water facilities could also be hit.
He later tempered the remarks, saying he did not want to pursue such action.
Blockade 'only for Iran'
The US president warned that the next strike could be a major one and suggested Washington could even "take over" Kharg Island.
Clarifying America's naval posture, Trump said the US blockade was directed solely at Iran.
"The blockade is only for Iran. Other countries can have whatever they want," he said.
Ceasefire under strain
Earlier in the day, Trump declared that the interim memorandum of understanding (MoU) with Iran was effectively "over," although he said diplomatic talks would continue.
His remarks came hours after the United States launched large-scale strikes on Iranian assets in Bandar Abbas, Sirik and Qeshm Island, saying the operation was in retaliation for Tehran's attacks on ships in the Strait of Hormuz.
Washington has also revoked a licence permitting the sale of Iranian oil.
Iran responded with strikes on Bahrain and Kuwait, raising fears that the fragile truce could collapse and push the Middle East into a broader regional conflict.