US President Donald Trump said the operation could continue for some weeks and it was unclear who was in charge in Iran, following the targeted killing of Supreme Leader Ayatollah Ali Khamenei in the opening hours of the US-Israel campaign over the weekend.
The attack on Iran has pitched the Gulf into war, killed scores of people in Iran, Israel and Lebanon, thrown global air transport into chaos and shut down shipping through the Strait of Hormuz, where a fifth of the world's oil trade skirts the Iranian coast, sending oil prices surging.
US Central Command announced 11 Iranian ships had been sunk, saying the Strait of Hormuz was not closed despite statements by Iran saying "if anyone tries to pass, the heroes of the Revolutionary Guards and the regular navy will set those ships ablaze".
Kuwait mistakenly shot down three American F-15E fighter jets during an Iranian attack, US Central Command said. All six crew members ejected and were safely recovered.
For Trump, the weekend strikes against a foe of the US and its allies for generations amounted to the biggest US foreign policy gamble in decades.
Six US service personnel had been killed, all in Iran's retaliatory attacks over the weekend on Kuwait. The total included two announced who were previously listed as unaccounted for.
The campaign could pose a major political risk for the president's Republican Party in this year's midterm elections, with only one-in-four Americans supporting the attack, according to a weekend Reuters/Ipsos poll.
Average US retail gas prices rose above $US3 ($A4.2) per gallon in part due to the conflict, a worrying sign for a president who already faces growing discontent over bread-and-butter issues.
Trump said he had ordered the attack to thwart Tehran's nuclear program and a ballistic missile program that he said was growing rapidly.
He gave no sign that the operation would end soon.
"Right from the beginning, we projected four-to-five weeks, but we have capability to go far longer than that," he said at the White House on Monday.
In the first formal Pentagon briefing since the campaign began, the chairman of the US Joint Chiefs of Staff, General Dan Caine, said more forces were still on their way to the region.
"This is not a single overnight operation. The military objectives ... will take some time to achieve, and in some cases will be difficult and gritty work," Caine said.
Iran denies seeking a nuclear weapon, and it said the US assault was unprovoked, occurring as Tehran and Washington were in negotiations on a nuclear accord. Trump withdrew from a prior international agreement curbing Iran's nuclear program during his first term in 2018.
Trump repeated his call to Iranians to rise up and overthrow their leaders but said it was unclear who was in charge.
Ali Larijani, Iran's top security official, said on social media that Iran wouldn't negotiate with Trump, who had "delusional ambitions" and "Iran, unlike the United States, has prepared itself for a long war".
Within Iran, where residents have jammed highways to flee the bombing, there was uncertainty about the future and emotion ranging from euphoria to apprehension and rage.
Conservative clerical leaders have shown no sign of yielding power, and military experts say airstrikes without ground forces may not be enough to drive them out.
Trump and US Defense Secretary Pete Hegseth on Monday did not rule out deploying ground forces to Iran.
The Israeli military said a wave of strikes in Tehran targeted Iranian security groups responsible for suppressing protests against the regime.
Meanwhile, scores of Iranians have been reported killed in strikes, including several that hit apparent civilian targets.
A new front in the war opened on Monday when the Lebanese Hezbollah militia launched missiles and drones towards Israel.
Israel responded with sweeping airstrikes, which it said targeted the Hezbollah-controlled southern suburbs of Beirut and struck senior militants. The Lebanese state news agency NNA said at least 31 people had been killed and 149 injured.
Israel declared Hezbollah leader Naim Qassem a "target for elimination".
Officials said they were not for now considering a ground invasion of Lebanon, whose government has banned military activities by Hezbollah.
As Washington's allies in the Gulf came under renewed attack from Iranian missiles and drones, black smoke rose above the area around the US embassy in Kuwait. There were loud blasts in Dubai and Samha in the United Arab Emirates, and in the Qatari capital Doha.
