Donald Trump says the US-Israeli operation in Iran could be a "four-week process" and he expects more American casualties after three troops were killed in action.
The deaths mark the first time US personnel have been killed in a major conflict since Mr Trump's return to the presidency.
"There will likely be more," Mr Trump said in a video message on the second day of US-Israeli strikes on Iran.
"But we'll do everything possible where that won't be the case.
"America will avenge their deaths and deliver the most punishing blow to the terrorists who have waged war against, basically, civilisation."
Few details about the deaths have been released, but multiple US outlets reported they were the result of Iranian strikes on a US military base in Kuwait.
Another five service members were seriously wounded, US Central Command said.
Iran launched a barrage of missiles at US bases and other targets across the Middle East after the US-Israeli strikes killed many of Iran's rulers, including supreme leader Ali Khamenei.
Mr Trump told the Daily Mail he believed fighting could continue for the next four weeks.
"We figured it will be four weeks or so," he was quoted as saying.
"It's always been about a four-week process so — as strong as it is, it's a big country, it'll take four weeks — or less."
Israel launched a new wave of strikes on Tehran on Sunday, local time. Israeli Prime Minister Benjamin Netanyahu said its attacks would "escalate in the days ahead".
Casualties mount across Middle East
Israeli authorities said 11 people had been killed, and more than 100 hurt, by Iran's retaliatory strikes.
Nine of the deaths were reported after a synagogue was struck in the central town of Beit Shemesh. The victims were sheltering in a safe room in the synagogue, emergency services said.
Deaths have also been reported in the United Arab Emirates, where Iranian drones killed at least three people.
Iran has declared the vital Strait of Hormuz shipping route closed, and its Islamic Revolutionary Guard Corps (IRGC) said it had hit three US and UK oil tankers in the Gulf.
A crew member on a Marshall Islands-flagged oil tanker was killed by a "suspected projectile" in waters near Oman.
"The vessel suffered an explosion and subsequent fire after being struck," shipping company V.Ships Asia said.
Shipping data showed hundreds of vessels, including oil and gas tankers, dropping anchor in nearby waters.
Trump says 48 leaders killed
Mr Trump, who has been monitoring the conflict from his Florida home, has not publicly commented on the American casualties.
But in a series of phone interviews with US news outlets, Mr Trump said the operation was making faster progress than expected.
The president told CNBC "things are evolving in a very positive way" and "ahead of schedule".
He told Fox News that 48 Iranian leaders had been killed. "Nobody can believe the success we're having, 48 leaders are gone in one shot."
On social media, Mr Trump said the US had destroyed nine Iranian naval ships and "largely destroyed their Naval Headquarters".
The IRGC said four ballistic missiles had hit an American aircraft carrier, the USS Abraham Lincoln, but the US military said that was a "lie".
"The missiles didn't even come close," US Central Command said.
The US said more than 1,000 targets were struck in the first 24 hours of the attack on Iran.
They included command and control centres, air defence systems, ballistic missile sites and headquarters of the Revolutionary Guard, according to the Department of Defense.
Iran and Trump 'agreed to talk'
Mr Trump meanwhile said he was preparing to talk to Iranian leaders.
"They want to talk, and I have agreed to talk, so I will be talking to them," he told the Atlantic.
"They could have made a deal. They should've done it sooner. They played too cute."
He did not say when or how such talks would take place, or who he hoped to speak to.
"Some of the people we were dealing with are gone, because that was a big — that was a big hit."
He later told the Daily Mail he did not know if the talks would happen soon.
"They want to talk, but I said you should have talked last week not this week."
Iran's president, Masoud Pezeshkian, said a leadership council composed of himself, the judiciary head and a member of the powerful Guardian Council had temporarily assumed Khamenei's duties.
Oman's foreign ministry said Iran had indicated it was open to de-escalation.
But on social media, Iranian Foreign Minister Abbas Araghchi suggested Iran was ready to keep fighting.
"We've had two decades to study defeats of the US military to our immediate east and west," he wrote.
"Bombings in our capital have no impact on our ability to conduct war."
Britain offers bases
The UK has said it would allow the US to use British bases to target Iranian missiles and launchers, but would "not join offensive action".
"We all remember the mistakes of Iraq," British Prime Minister Sir Keir Starmer said. "And we have learned those lessons."
The European Union called for "maximum restraint" after a meeting of foreign ministers on Sunday.
"The events unfolding in Iran must not lead to an escalation that could threaten the Middle East, Europe and beyond," an EU statement issued after the meeting said.
The statement condemned Iran's repression of citizens, ballistic missile and nuclear programs, and retaliatory attacks. But it did not express support for the US-Israeli strikes.
The foreign ministers of Qatar, Saudi Arabia, the UAE, Kuwait, Oman and Bahrain also held a virtual emergency meeting, and later called on Iran to immediately halt attacks on their territories.
The top Gulf diplomats said their countries retained "their legal right to respond and the right to self-defence" according to international laws.
Demonstrations turn deadly
Protests against the US-Israeli strikes have turned violent in Pakistan and Iraq.
At least 23 protesters were killed in clashes in Pakistan yesterday. Ten died in the port of Karachi, where security guards at the US consulate fired on demonstrators who breached the outer wall.
Another 11 people were killed in the northern city of Skardu, where a crowd torched a UN office.
Two more deaths were reported in the capital, Islamabad.
In Iraq, police fired tear gas and stun grenades to scatter hundreds of pro-Iranian protesters outside the Green Zone diplomatic compound in Baghdad, where the US embassy is located.
Meanwhile, snap polling in the US found just over a quarter of respondents approved of the US strikes.
In a Reuters/Ipsos poll of 1,282 Americans, only 27 per cent said they approved of the strikes, while 43 per cent disapproved and 29 per cent were unsure.
Mr Trump has said the attack was intended to ensure Iran could not have a nuclear weapon, to contain its missile program and to eliminate threats to the US and its allies.
He has yet to lay out his longer-term aims in Iran, which faces a power vacuum that could leave it in chaos.
Thousands of Iranians were killed in a crackdown authorised by Khamenei against anti-government protests in January.
ABC/wires
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