But while the remarks from the two leaders provided hope for an end to the month-long crisis, crude prices jumped on lingering worries about the closure of the strategic Strait of Hormuz.

They also come as the economic impact of the conflict worsens, with average US gasoline prices topping $4 a gallon for the first time in four years, European inflation spiking, and governments unveiling a range of support measures.

Trump told reporters in the Oval Office the United States would be leaving Iran "very soon", perhaps within "two weeks, maybe three".

"But we're finishing the job," he insisted.

"We want to knock out every single thing they have," Trump said, before adding that "it's possible that we'll make a deal before that."

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The White House also said he would address the nation at 0100 GMT Thursday "to provide an important update on Iran".

Earlier, Iranian leader Masoud Pezeshkian told the head of the European Council the country had "the necessary will to end this conflict, provided that essential conditions are met -- especially the guarantees required to prevent repetition of the aggression".

Wall Street surged, with the Nasdaq up 3.8 percent and the S&P 500 adding almost 3 percent.

In Asia, Seoul -- the standout before the war but among the worst-hit since it started -- was up more than 6 percent, while Tokyo and Taipei gained at least 4 percent.

Hong Kong, Shanghai, Sydney, Singapore, Manila and Jakarta were also sharply higher.

Traders appeared to brush off Prime Minister Benjamin Netanyahu's comments that Israel would press ahead with its campaign and that "we will continue to crush the terror regime".

However, Trump also said US forces would not work to unblock the Strait of Hormuz, through which a fifth of global oil and gas passes, and said it was up to other countries to do so.

"What happens with the strait we're not going to have anything to do with," he said.

In a Truth Social post earlier Tuesday, Trump lashed out at NATO allies and other countries that have refused to help the United States secure the waterway.

"The U.S.A. won't be there to help you anymore, just like you weren't there for us," he wrote. "Iran has been, essentially, decimated. The hard part is done. Go get your own oil!"

The remarks came after he said Monday he was willing to end the war even if the strait remained closed.

Trump has zigzagged on whether Washington plans to escalate the conflict -- possibly by deploying American ground forces -- or try to end it through negotiations.

Still, City Index's Fiona Cincotta warned in a commentary: "Even if outright military tensions ease, the economic damage from elevated oil prices may already be feeding through.

"With oil still above $100 a barrel, higher energy costs are likely to tighten financial conditions, raise inflation pressures, and weigh on growth."

She added that "diplomatic signals remain mixed, and as long as uncertainty persists and shipping disruptions remain in place, oil prices are likely to stay elevated".

Both main crude contracts rose more than one percent Wednesday, a day after Brent dived more than three percent and West Texas Intermediate shed 1.5 percent.

That came as more US troops continued to arrive in the region, and after the Wall Street Journal cited Arab officials as saying the United Arab Emirates was preparing to help Washington open the Strait by force, which would make it the first Gulf nation to join the battle.

The report said the UAE, which has been targeted by Iran during the war, was lobbying for a United Nations Security Council resolution to authorize such action.

The head of maritime analyst group Kpler told AFP Asia faced the gravest fallout from the war.

"We think Asia will, for now, be the ones suffering the most," president Jean Maynier said.

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