Speaking to reporters aboard Air Force One on Saturday, Trump said he is not interested in negotiating with Iran at this point and later added the air campaign could make it a moot point if all potential leaders of Iran are killed and the Iranian military is destroyed.
"At some point, I don't think there will be anybody left maybe to say 'We surrender,'" Trump said.
Trump's remarks came on a day of Israel and Iran trading numerous attacks as the Middle East war entered a second week. Iran's president apologised to neighbouring states to cool anger across the Gulf but stirred criticism from hardliners at home.
"I personally apologise to neighbouring countries that were affected by Iran's actions," Iranian President Masoud Pezeshkian said, urging them not to join US-Israeli attacks on Iran.
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.
Trump nonetheless cast Iran's apology as a surrender, while saying the country would be "hit very hard" on Saturday and warning the US could widen its attacks.
Amid possible divisions within Iran's leadership over Pezeshkian's remarks, Israeli Prime Minister Benjamin Netanyahu, in a televised address, said any Iranian Revolutionary Guards who lay down their arms would be unharmed.
Netanyahu also said: "We stand by all countries attacked by Iran; many are talking to us."
Pezeshkian's comments caused a political stir in Iran, prompting his office to reiterate Iran's military would respond firmly to attacks from U.S. bases in the region.
Hours later, the president repeated his statement on social media but left out the apology from his speech that had angered hardliners, including the powerful Revolutionary Guards.
Hours after Pezeshkian's announcement, Iran's Revolutionary Guards said their drones struck a US air combat centre at Al Dhafra Air Base near Abu Dhabi, capital of the United Arab Emirates. Reuters could not independently verify that report.
Late into the night, the Guards targeted an Israeli refinery, according to state media. Air raid sirens sounded in the Haifa area, but there were no reports of destruction.
There were reports of rockets targeting the US embassy in Baghdad, security sources and witnesses said. Iraqi Prime Minister Mohammed Shia al-Sudani ordered his security forces to pursue those responsible, according to a statement.
The Associated Press reported one missile landed on a helicopter landing pad in the large complex, without casualties.
In Iran, local news agencies, citing an Iranian Oil Ministry source, said its fuel depots were hit by strikes in three areas, including Karaj, west of Tehran.
The UAE, Kuwait, Qatar, Bahrain, Oman, Saudi Arabia and Iraq have all reported drone or missile attacks over the past week.
With the conflict spreading, Israel warned Lebanon of a "very heavy price" if it did not rein in Hezbollah, as it pounded the group's strongholds with airstrikes and mounted a deadly airborne raid in the east.
The total death toll from Israel's attacks on Lebanon since Monday has risen to 294, the health ministry said. The US-Israeli attacks have killed at least 1332 Iranian civilians and wounded thousands, according to Iran's United Nations ambassador Amir Saeid Iravani.
Huge explosions were heard in parts of Tehran, state media reported, while Israel said it had struck Iranian missile sites and command centres.
Ayatollah Hossein Mozafari, one of the 88-member Assembly of Experts, the clerical body charged with choosing the next leader, was quoted as saying the assembly could meet in the next 24 hours to decide.
