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Iran had pledged the US would regret sinking one of its warships on Thursday.
The US President responded to Iran's threats by calling on members of the Iranian Revolutionary Guard Corps, the military and police to surrender their weapons or suffer the same fate as Ayatollah Ali Khamenei.
Speaking at the White House, Mr Trump said: "I'm once again calling on all members of the Iranian Revolutionary Guard, the military and the police to lay down their arms.
"You'll be perfectly safe with total immunity or you'll face absolutely guaranteed death, and I don't want to see that."
Mr Trump also suggested Iran has made contact to "make a deal" to end the US military operation.
He said: "They're calling, they're saying, 'How do we make a deal?'
"I said, 'You're being a little bit late,' and we want to fight now more than they do."
The US leader revealed that his country has obliterated 24 Iranian vessels within three days.
"The United States military, together with the wonderful Israeli partners, continues to totally demolish the enemy, far ahead of schedule and at levels that people have never seen before," he said.
Mojtaba Khamenei, the second eldest son of the former Supreme Leader Khamenei, is tipped to be his successor. Mr Trump stated he would choose a new leader and Mojtaba was "unlikely".