Iran threatened the US president on Tuesday, rejecting his warnings from the previous day and promising that not a single drop of oil would leave the Middle East "until further notice".

"Iran is not afraid of your empty threats. Those more powerful than you have tried to eliminate the Iranian nation and have not succeeded. Be careful not to be eliminated yourself!" wrote Ali Larijani, head of Iran's Supreme National Security Council, on X.

The Islamic Republic dismissed Donald Trump's remarks on Monday, in which he spoke of the war being "virtually" over and vowed to strike "harder" if Tehran continued to paralyze oil flows in the region.

This prospect is causing anxiety in the markets, in the face of a conflict that has been engulfing the Middle East since February 28.

"The Iranian armed forces (...) will not allow the export of a single liter of oil from the region to the enemy camp and its partners until further notice," said Ali Mohammad Naini, spokesman for the Revolutionary Guards, the ideological army.

The Iranian government de facto controls the highly strategic Strait of Hormuz, through which a fifth of the world's oil and liquefied natural gas (LNG) production passes.

And he is showing his determination after appointing Ayatollah Mojtaba Khamenei as the new supreme leader on Sunday, ten days after his father was killed by Israeli-American strikes in which he himself was injured.

Efforts "to reduce and control the price of oil and gas will be temporary and futile. In times of war, trade is dependent on regional security," the spokesman for the Revolutionary Guards asserted, according to the Tasnim news agency.

They even promised to allow passage through the precious passage "any Arab or European country that expels the Israeli and American ambassadors from its territory".

These remarks stand in stark contrast to those made by Donald Trump the previous day. "The war will end soon," he had asserted, during his first press conference since the start of the conflict.

Leaving, as often, doubt hanging over his plans, he threatened to strike Iran "much harder" if Tehran "held the world hostage" by blocking the Strait of Hormuz.

The US president also announced that he would lift some oil sanctions "in order to reduce prices" which have soared in recent days. He did not specify which sanctions he was referring to, nor which countries were affected.

- "Rare" market volatility -

Indeed, black gold was on everyone's lips on Tuesday.

The resumption of traffic in the Strait of Hormuz is "absolutely crucial," said the CEO of Saudi oil company Aramco, warning of potentially "catastrophic consequences" of a prolonged blockade on oil markets.

Qatar has denounced attacks on energy facilities "on both sides", which it says constitute "a dangerous precedent".

India has made the same observation regarding the disruption of gas supply and has decided to allocate it primarily to household consumption and transportation.

While awaiting further developments, global markets reversed course after Monday's panic. Oil prices fell 5% at the close of Asian trading, and European gas lost 15%.

European stock markets, in unison, rebounded at the opening. Paris, Frankfurt and London gained between 1.29% and 2.04%, following the recovery of Asian stock markets (Seoul +5.35%, Tokyo +2.88%).

Analysts are struggling to make sense of it all, amidst contradictory statements and indiscriminate attacks. "It's rare for markets to experience such volatility," notes Ipek Ozkardeskaya, an analyst for Swissquote Bank.

Donald Trump's remarks helped to halt the market decline. But the conflict continues "at full speed (...) and the intentions of the United States in this war remain unclear."

- "Breaking the bones" -

Israel will "break the bones" of Iranian power, but is "not finished" with it yet, Israeli Prime Minister Benjamin Netanyahu said.

His army announced a new series of strikes on Tehran, where AFP journalists heard explosions shortly afterwards.

It also continues to strike Lebanon, saying it is targeting the strongholds of the pro-Iranian Hezbollah movement in the south and east of the country, a collateral victim of the war with Iran.

Israeli forces warned of strikes on Tyre and Sidon (south) against the movement, calling on residents of several buildings to evacuate their homes.

This is a now common scenario, particularly for Beirut, whose southern suburbs have been virtually emptied. More than 667,000 people have been displaced by Israeli strikes on its neighbor, including 100,000 in 24 hours, according to the UN High Commissioner for Refugees (UNHCR).

The Gulf monarchies are trying, as best they can, to protect hydrocarbon infrastructure that is constantly under attack.

The United Arab Emirates reported that a drone attack had caused a fire in an industrial area. Kuwait and Saudi Arabia said they had themselves shot down unmanned aerial vehicles, which are ubiquitous in the conflict. And Bahrain reported two deaths in an attack on a residential building.

In the latest sign of the risk of regional escalation of the conflict, a second Iranian missile was intercepted on Monday over Turkey. Iranian President Massoud Pezeshkian proposed to his Turkish counterpart, Recep Tayyip Erdogan, that a joint team investigate these incidents, according to Iranian media.

Without confirming, Turkey announced the deployment of a Patriot air defense system in the center of the country "to support the protection of (its) airspace".