Shortly after Trump told reporters aboard Air Force One he was not interested in negotiating an end to the conflict that has roiled oil markets, hurt business and snarled global travel, US ally Israel announced fresh strikes across Iran that it said had hit critical fuel storage sites.
"At some point, I don't think there will be anybody left maybe to say 'we surrender'," Trump said.
The governments of Saudi Arabia, Kuwait, the United Arab Emirates and Bahrain reported Iranian drone attacks in their countries on Saturday and early Sunday, with a huge fire engulfing a government office block in Kuwait.
Saudi Arabia has told Tehran continued Iranian attacks on the kingdom and its energy sector could push Riyadh to respond in kind.
In an apparent attempt to cool anger across the Gulf, Iran's president apologised to neighbouring states for its attacks on US facilities in those countries on Saturday.
He dismissed Trump's demand for the Islamic Republic's unconditional surrender as "a dream", but said its temporary leadership council had agreed to suspend attacks on nearby states unless strikes on Iran originated from their territory.
Pezeshkian's comments caused a political stir in Iran, prompting his office to reiterate Iran's military would respond firmly to attacks from US bases.
The clerical body charged with choosing Iran's next supreme leader, to replace Ayatollah Ali Khamenei, slain in an attack last week, could meet as soon as Sunday, Iranian media reported.
A majority consensus over a successor has more or less been reached, Assembly of Experts member Ayatollah Mohammadmehdi Mirbaqeri said, according to the Mehr news agency.
Trump has justified the biggest US military operation in the Middle East since the 2003 invasion of Iraq by saying Tehran posed an imminent threat to the US, without providing evidence.
He has also said Iran was too close to being able to build a nuclear weapon.
The US and Israel have discussed sending special forces into Iran to secure its stockpile of highly enriched uranium at a later stage of the war, Axios reported, citing four people with knowledge of the discussions.
Asked about the possibility of sending ground troops to secure nuclear sites on Saturday, Trump said it was something they could do "later on".
Huge explosions were heard in parts of Tehran, state media reported, while Israel said it had struck Iranian missile sites, command centres and fuel depots on Saturday.
The US-Israeli attacks have killed at least 1332 Iranian civilians and wounded thousands, Iran's United Nations ambassador Amir Saeid Iravani said.
US forces were likely responsible for an apparent strike on an Iranian girls' school that killed scores of children, US officials have told Reuters.
Trump, without citing evidence, said Iran was responsible.
Defense Secretary Pete Hegseth said the matter was still under investigation.
Iranian attacks have killed 10 people in Israel.
At least six US service members have been killed. Their remains arrived on Saturday at an Air Force base in Delaware.
Iran said on Sunday it had struck US bases in Kuwait.
It also hit a desalination plant in Bahrain.
An Iranian Oil Ministry source told local news agencies fuel depots in three areas including Karaj, west of Tehran, were hit by strikes.
With the conflict spreading, Israel has launched fresh attacks in Lebanon after the Iran-aligned militia Hezbollah fired across the border.
Israel warned Lebanon of a "very heavy price" if it did not rein in Iran-allied Hezbollah militants, as the death toll from Israel's attacks on Lebanon since Monday rose to about 300.
Iran's apparent strategy of maximum chaos has driven up the costs of the conflict by raising energy prices, hurting global business and logistics links and disrupting air travel.
