Miami, Florida - President Donald Trump said Monday in an interview with CBS that the war with Iran was "very complete" and that the US was far ahead of his initial timeline of around a month.

US stocks jumped higher, and oil prices sank in after-hours trading following Trump's comments, despite the fact that there were no immediate signs of the conflict abating.

"I think the war is very complete, pretty much. They have no navy, no communications, they've got no air force," Trump told CBS News by phone.

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"Their missiles are down to a scatter. Their drones are being blown up all over the place, including their manufacturing of drones," he added. "If you look, they have nothing left. There's nothing left in a military sense."

Trump told the broadcaster that the US was "very far" ahead of his initially stated war timeframe of four or five weeks.

The US leader has given similar assessments in recent days of battle damage from the US-Israeli strikes that began on February 28, but had not gone as far in saying that the war was nearing an end.

Just last Friday, Trump issued a statement that Iran's "unconditional surrender" was the only acceptable outcome for ending the war.

And his comments came about an hour after the Pentagon posted on social media that the US had "only just begun to fight."

CBS reported that when asked if he thought the war could wrap up soon, Trump answered: "Wrapping up is all in my mind, nobody else's."

Trump also threatened Iran if it tried to close the Strait of Hormuz, the shipping lane where oil tanker transit has already virtually halted, sending energy prices soaring around the world.

He said he was "thinking about taking it over" even as he insisted that traffic was starting to move.

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The US president, however, had few words for Iran's new supreme leader Ayatollah Mojtaba Khamenei, who was elected to replace his slain father Ali Khamenei.

"I have no message for him. None, whatsoever," Trump said, adding that he had someone else in mind to lead Iran.

Trump earlier told the New York Post he was "not happy" with Mojtaba Khamenei's appointment.