Shortly after the United States urged Americans to flee all Middle Eastern nations from Egypt eastward, two drones hit the US embassy in Riyadh, sparking a quick vow by Trump to retaliate "soon", without elaborating how.

New powerful explosions shook windows in Tehran throughout the night as fighter jets flew over the Iranian capital, AFP journalists witnessed, and the Pentagon said it had achieved air superiority over the country, ruled since 1979 by Islamic clerics virulently opposed to the United States.

Beyond launching missile and drone attacks that forced Qatar's state-run energy firm to halt liquefied natural gas production, Tehran also vowed to choke one of the world's most vital shipping lanes.

"We will burn any ship that tries to pass through the Strait of Hormuz," Revolutionary Guards General Sardar Jabbari said of the strategic waterway to the Gulf through which about 20 percent of global seaborne oil travels.

Trump said that the war, which began Saturday with a strike that killed Iran's supreme leader, Ayatollah Ali Khamenei, was going "substantially" ahead of schedule but that the United States was equipped for a prolonged conflict.

"From the beginning we projected four to five weeks, but we have capability to go far longer than that," Trump said at the White House.

-- 'Won't take years' --

The US president laid out for the first time the operation's objectives -- destroying Iran's missiles, navy and nuclear programme and stopping its support for armed groups across the region. The goals notably did not include toppling the Islamic republic, even though on Saturday Trump had urged the people of Iran to rise up and overthrow their government.

As Iran ramped up its retaliation, Saudi Arabia, home to one of the region's largest oil refineries which has already been closed following an attack, said it intercepted eight more drones in two cities, including the capital, on Tuesday.

The Saudi defence ministry confirmed two drones attacked the US embassy, which said that caused "a limited fire and minor material damage".

Speaking to the NewsNation network, Trump said "you'll find out soon" how the United States would respond, without providing further detail.

The US mission in Riyadh asked its citizens in the capital as well as the cities of Jeddah and Dharan to shelter in place, while the US State Department ordered its "non-emergency" staff and their families to leave Bahrain, Jordan and Iraq.

Qatar, which had comparatively good relations with Iran before the war, said it shot down two Iranian bombers, the first time a Gulf Arab country has hit planes from their giant neighbour.

The Israeli military for the second day carried out strikes on Lebanon, with its military saying it was targeting Iran-backed Hezbollah after the militant group claimed rocket and drone attacks on Israel.

As the conflict spread, Israel's Prime Minister Benjamin Netanyahu said its strikes with the United States on Iran would continue but not become "an endless war".

"It may take some time, but it's not going to take years," he told Fox News in an interview broadcast Monday.

-- 'Imminent threat?' --

Secretary of State Marco Rubio presented a strikingly new narrative of how the conflict started, saying on Monday that the United States, which built up its military to levels not seen since its 2003 Iraq invasion, attacked only after learning that ally Israel was set to strike Iran.

Iran had been ready to strike US forces in the region in response to Israel, so Trump decided to intervene "pre-emptively" alongside Israel, Rubio said.

"The imminent threat was that we knew that if Iran was attacked -- and we believed they would be attacked -- that they would immediately come after us," Rubio told reporters before briefing lawmakers.

Rival Democrats voiced disbelief, with Senator Mark Warner saying it was "unchartered territory" for the United States to be triggered into action by Israel's perception of a threat.

Iran's foreign minister Seyed Abbas Araghchi responded that "there was never any so-called Iranian 'threat'."

"Mr. Rubio admitted what we all knew: U.S. has entered a war of choice on behalf of Israel'," he posted on X.

Netanyahu alleged on the interview with Fox that Iran had been working on new weapons sites since a 12?day conflict in June, when Israel and the United States also launched coordinated strikes on the Islamic republic.

In an earlier interview with the New York Post, Trump -- who campaigned on promises to end US involvement in wars -- refused to rule out deploying US ground troops to Iran "if they were necessary."

- Death toll rises -

Israel's military issued new evacuation orders for dozens of locations in Lebanon on Tuesday, following explosions rocking the capital the previous day as Israeli warplanes struck Beirut's southern suburbs and the south of the country.

The Lebanese government said at least 52 people were killed in the strikes that came after Hezbollah, the armed Shiite movement affiliated with Iran, launched rockets and drones toward Israel in retaliation for Khamenei's death.

In response, Lebanese Prime Minister Nawaf Salam took the unprecedented step of ordering an "immediate prohibition" of Hezbollah's military activities and called on the group to hand over its weapons.

Throughout the region, the death toll has steadily increased with six US military personnel killed so far in the war, according to US Central Command.

Iranian media have reported hundreds of Iranian casualties, including at a girl's school, although AFP reporters have not been able to verify tolls independently.

The US-based Human Rights Activists News Agency (HRANA) on Tuesday said there were 101 casualties inside Iran on the third day of the war, including "85 civilian deaths and 11 military personnel killed".

Many residents in Tehran were torn between fear of the bombings and hope that the government's days might now be numbered. AFP journalists witnessed some residents with suitcases in hand preparing to leave the unusually quiet capital on Monday.

"Every time we hear the noises, we get scared for just a second," a 45-year-old lawyer said in a voice message to Europe, "but we experience some joy and excitement every time we hear a hit."

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