The war had sent stock markets slumping and oil prices soaring on Monday as Tehran, under new leader Mojtaba Khamenei, fired a fresh barrage of missiles at its Gulf neighbours and signaled that the strategic Strait of Hormuz would likely remain closed.

But Wall Street climbed into positive territory on Trump's signals of a short war, with Tokyo and Seoul also opening strongly Tuesday, despite the president's continued threats to expand the campaign if Iran did not fall in line.

Oil prices also reversed course, falling as much as five percent a day after benchmark crude rocketed past $100 a barrel -- its highest level since Russia's invasion of Ukraine in 2022.

"It's going to be ended soon, and if it starts up again they'll be hit even harder," Trump told a news conference in Florida, after telling lawmakers that the campaign would be a "short-term excursion."

Iran's Revolutionary Guards replied Tuesday that they, not the Americans, would "determine the end of the war".

Trump's remarks came on the first day in power for the 56-year-old son of slain leader Ali Khamenei, with Iranian forces launching a fresh wave of missile and drone attacks on Saudi Arabia, Bahrain, Qatar, the UAE and Israel.

Another missile was also fired at NATO member Turkey, the second such incident in five days, with the alliance's air defenses intercepting it before it could reach its target.

Diplomatic efforts focused Monday on the highly strategic Strait of Hormuz, which has been blocked to nearly all oil tankers -- sending shockwaves across the global economy.

French President Emmanuel Macron said his country and its allies were working on a "purely defensive" mission to reopen the strait, through which nearly 20 percent of the world's crude oil usually transits.

The mission would aim to escort ships "after the end of the hottest phase of the conflict," but experts say it would mean putting naval vessels at risk of fire from the nearby Iranian coast.

Kamal Kharazi, a foreign policy adviser to Iran's supreme leader, told CNN that Tehran was calculating that economic pressure would eventually prompt other countries to intervene and end the war.

- Rallies -

Iran faced a fresh blitz of US and Israeli strikes after its Assembly of Experts, the top clerical body, appointed its first new supreme leader in 37 years.

Iranian state media carried images of tens of thousands of people celebrating Mojtaba Khamenei's selection in central Tehran, many carrying his picture.

Iran's rebel Houthi allies in Yemen and the Hezbollah armed group in Lebanon pledged allegiance, while Russian President Vladimir Putin on Monday promised "unwavering support".

Trump told reporters he was "disappointed" about Khamenei's appointment, but remained open to a replacement from inside the Islamic republic, citing the recent transition of power in Venezuela as "a formula that has been very good so far."

Ali Ansari, a professor of Iranian history at the University of St Andrews in Scotland, told AFP the new supreme leader was a hardliner who had "been involved in all the most violent repressions that have taken place over the last 15-16 years".

- Oil risks -

Oil traders, policymakers and central bankers are all watching the Middle East for news about Gulf energy infrastructure, which is crucial for the world economy.

About 10 vessels in or near the Strait of Hormuz have come under attack since Iran blocked the waterway 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, meaning goods sitting on ships would be unloaded.

Following strikes on Bahrain's Al Ma'ameer oil facility that ignited a fire, the country's state-owned energy company Bapco joined its 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.

- 'Resistance' -

In Bahrain, the interior ministry said early Tuesday an Iranian attack on a residential area in the capital Manama killed one person and injured others.

In Israel earlier, around 10 explosions were audible in Tel Aviv after the military announced it had detected missiles inbound from Iran.

At least one Israeli was killed when he was hit by shrapnel, emergency services said.

Israel said Tuesday that it had struck an Iranian missile launcher shortly after a barrage fired from the Islamic republic triggered air raid warnings in several Israeli areas.

The multi-front war also intensified in Lebanon, where Israeli and Hezbollah exchanges of fire since March 2 have killed at least 486 people and wounded more than 1,300.

Lebanese President Joseph Aoun accused Hezbollah of working to "collapse" the state, while the head of the group's parliamentary bloc said it had "no other option...than the option of resistance."

burs-arp/jgc