Markets jumped when Trump suggested to CBS News that the US-Israeli assault was "very complete," but during a later speech and press conference he offered shifting accounts of what to expect.

"I think soon. Very soon," Trump told reporters at his Doral National golf club near Miami, Florida, when asked if he thought the war could end in days or weeks.

"Everything they have is gone including their leadership."

But Trump also pressed for what he called "ultimate victory" against Tehran's clerical establishment, which over the weekend picked the son of slain supreme leader Ali Khamenei as its new chief.

Trump said the United States was saving some of the "most important" targets in Iran for possible later strikes if needed, including the country's electrical grid.

The US leader also threatened an attack of "incalculable" size if Tehran blocks oil supplies coming through the Strait of Hormuz, as crude prices spike over the Middle East war.

"And if Iran does anything to do that, they'll get hit at a much, much harder level," Trump told the news conference

"We will hit them so hard that it will not be possible for them or anybody else helping them to ever recover that section of the world, if they do anything."

At the same time Trump played down the scale of the conflict, which has not been approved by the US Congress, repeatedly calling it an "excursion" rather than a war.

Republican Trump has faced criticism over the mixed messages coming from his administration about the goals of the Iran war, particularly over whether he is seeking full-scale regime change or not.

He declined to say whether new leader Mojtaba Khamenei had a target on his back, saying only that his appointment was "not good."

But the US president, who has said he should be involved in picking Iran's new leader in the same way as with Venezuela in January, said he preferred an "internal" candidate rather than an external one.

Trump added that he had a "positive phone call with Russian President Vladimir Putin on the Ukraine and Iran wars.

"He wants to be helpful" on the Middle East, Trump said of Putin, who backs Iran and invaded Ukraine in 2022.

Earlier, Trump's comments to broadcaster CBS that the United States was far ahead of his initial timeline of around a month had sparked optimism on the stock and oil markets.

"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.

"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 US broadcaster that the United States was "very far" ahead of his initially stated war time frame 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 United States had "only just begun to fight."

Yet in his speech to Republican leaders at Doral shortly after the CBS interview, Trump again appeared to hint at more conflict to come.

"We've already won in many ways, but we haven't won enough," Trump said.