The Israeli military said it killed a senior commander of Iran's elite Quds Force on Tuesday in a strike on Tehran, adding that he was responsible for its operations in Lebanon.

"Earlier today, the Israeli Air Force... struck and eliminated the temporary commander of the Lebanon Corps of the Iranian Quds Force, Daoud Ali Zadeh, in Tehran," a military statement said, adding that Ali Zadeh was "the highest-ranking Iranian commander responsible for Lebanon".

French President Emmanuel Macron on Tuesday ordered France’s nuclear-powered aircraft carrier to move from the Baltic Sea to the Mediterranean to help protect allied assets during the ongoing war in the Middle East.

Noting that the war had spread to Lebanon, Macron said the Iran-backed militant Hezbollah group made “the grave mistake of striking Israel” and putting the Lebanese people in danger but warned against Israel launching a ground operation.

French President Emmanuel Macron said Tuesday that the United States and Israel's military operations in Iran were conducted "outside international law", but placed primary blame on the Islamic republic.

"The United States of America and Israel decided to launch military operations, conducted outside international law, which we cannot approve of," said Macron.

US and Israeli strikes pummeled targets across Tehran on Tuesday, as President Donald Trump warned it was "too late" for Iran to seek talks to escape a war now in its fourth day.

Drones and missiles crashed into oil facilities and US embassies in the Gulf as the Islamic republic retaliated, and Israel pushed troops deeper into Lebanon to battle the Tehran-backed militia Hezbollah after it entered the fray.

New strikes were reported Tuesday across the Middle East, including Israeli bombardment on Lebanon and a drone attack on the U.S. embassy in Saudi Arabia's capital Riyadh.

The conflict started with U.S. and Israeli strikes on Iran over the weekend, which sparked retaliatory Iranian attacks across the region, and showed no sign of abating as it entered its fourth day.

The Palestinian Islamic Jihad’s armed wing said on Monday that its commander in Lebanon was killed in Israeli strikes on Beirut’s southern suburbs.

In a statement, the Quds Brigades said Adham Adnan al-Othman, the head of the armed wing in Lebanon, was killed "as a result of the treacherous Zionist aggression that targeted the southern suburbs of Beirut, at dawn on Monday".

The war launched by the United States and Israel against Iran spread across the Middle East and beyond on Monday, with Lebanon's Hezbollah entering the fray and a British air base in Cyprus targeted.

Iran’s army said Monday it targeted US Ali Al Salem air base in Kuwait as well as vessels in the Indian ocean after the killing of the Islamic republic’s supreme leader in U.S. and Israeli strikes.

"Missile units of the army’s ground and naval forces operating from various locations targeted the U.S. Ali Al Salem air base in Kuwait as well as enemy vessels in the northern Indian Ocean over the past hours," the army said in a statement.

Israel and Hezbollah traded fire on Monday, while President Donald Trump vowed to avenge the deaths of U.S. service members and said the war with Iran could last for weeks.

The European Union has warned of the cost to the Middle East of a long war, and said it was reinforcing its naval mission in the Red Sea.

The U.S. military on Sunday said three service members have been killed and five seriously wounded in the operation against Iran -- the first casualties of any kind announced on the U.S. side.