As the crisis in the crude-rich Middle East continued into a second week, with seemingly little sign of a conclusion on the horizon, the US president said the campaign was far ahead of his initial timeline of around a month.

"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.

"If you look, they have nothing left. There's nothing left in a military sense," he added.

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.

He later told a news conference in Florida that "it's going to be ended soon, and if it starts up again they'll be hit even harder".

When asked if he thought the war could end in days or weeks, he replied: "I think soon. Very soon."

The US leader also threatened an attack of "incalculable" size if Tehran blocks oil supplies coming through the Strait of Hormuz, through which a fifth of global supplies pass.

His remarks come just days after he issued a statement saying Iran's "unconditional surrender" was the only acceptable outcome for ending the war, which sent shivers through markets fearing a prolonged conflict.

Still, Iran's Revolutionary Guards responded by saying they, not the Americans, would "determine the end of the war".

Investors jumped on the comments, sending crude prices plunging around 10 percent Tuesday before they pared the losses to around five percent.

That came a day after extreme swings that saw the commodity rocket 30 percent to a peak above $119 a barrel before plunging to as low as $84.

The recovery had already begun earlier Monday after it emerged that finance ministers from the Group of Seven industrialised nations would discuss tapping stockpiles to ease supply constraints.

Trump also said he would waive some oil-related sanctions, after acknowledging talks with Russian counterpart Vladimir Putin. Moscow has been hit with a range of measures to limit its crude exports since its invasion of Ukraine in 2022.

- 'Incredibly wild ride' -

"We're looking to keep the oil prices down," Trump said. "They went artificially up because of this excursion."

White House officials reassured G7 partners that the move would only be temporary.

And Asian stock markets rallied, with Seoul up more than five percent and Tokyo 2.9 percent. There were also advances in Hong Kong, Shanghai, Sydney, Singapore, Bangkok, Mumbai, Taipei, Manila and Jakarta.

That came after all three main indexes on Wall Street ended sharply higher, having reversed early heavy selling, though futures slipped Tuesday.

Meanwhile, diplomatic efforts focused on the Strait of Hormuz, which has been blocked to nearly all oil tankers.

French President Emmanuel Macron said Monday France was working with allies on a "purely defensive" mission to reopen the waterway.

About 10 vessels in or near the Strait of Hormuz have come under attack since Iran blocked the strait in retaliation for the US-Israeli strikes, shipping experts say.

Global shipping giant MSC announced it was formally halting some export shipments from the Gulf, while Bahrain's state-owned energy company Bapco joined counterparts in Qatar and Kuwait in declaring "force majeure" -- a warning that events beyond its control may lead it to miss export targets.

The Saudi defence ministry said Monday it had thwarted a drone attack targeting an oil field in the kingdom's east, near the Emirati border.

"It has been an incredibly wild ride for traders and investors to navigate the price action put to them over the past 24 hours, with breathtaking reversals taking place across many parts of the financial markets," said Chris Weston, an analyst at Pepperstone.

"The pressure valve has clearly been released for now. However, volatility across energy markets remains exceptionally elevated.

"While the most extreme stress has eased, markets are still pricing a significant degree of uncertainty and risk.

"The geopolitical backdrop remains fluid, and traders should expect volatility to remain a defining feature of the trading environment in the days ahead."

- Key figures at around 0700 GMT -

West Texas Intermediate: DOWN 5.3 percent at $89.72 per barrel

Brent North Sea Crude: DOWN 5.2 percent at $93.78 per barrel

Seoul - Kospi: UP 5.4 percent at 5,532.59 (close)

Tokyo - Nikkei 225: UP 2.9 percent at 54,248.39 (close)

Hong Kong - Hang Seng Index: UP 1.9 percent at 25,893.26

Shanghai - Composite: UP 0.7 percent at 4,123.14 (close)

Euro/dollar: UP at $1.1631 from $1.1614 on Monday

Pound/dollar: UP at $1.3451 from $1.3427

Dollar/yen: DOWN at 157.54 yen from 157.85 yen

Euro/pound: UP at 86.52 pence from 86.49 pence

New York - Dow: UP 0.5 percent at 47,740.80 (close)

London - FTSE 100: DOWN 0.3 percent at 10,249.52 (close)

dan/mtp

Dow