Trump's comments came hours after Iranian President Masoud Pezeshkian posted on social media that unnamed countries had begun mediation efforts, briefly raising hopes of a resolution a week after the US and Israel launched strikes on Iran.
"There will be no deal with Iran except UNCONDITIONAL SURRENDER!" Trump wrote on his Truth Social platform on Friday.
"After that, and the selection of a GREAT & ACCEPTABLE Leader(s), we, and many of our wonderful and very brave allies and partners, will work tirelessly to bring Iran back from the brink of destruction, making it economically bigger, better, and stronger than ever before."
Trump has offered shifting explanations of his war aims, raising the possibility of an extended conflict that has already spilled well beyond Iran's borders, shaken global financial markets and sent oil prices soaring.
Iran has responded by hitting Israel and Gulf states that host US military installations.
The US-Israeli attacks had killed at least 1332 Iranian civilians and wounded thousands, according to Iran's UN ambassador, Amir Saeid Iravani.
Iranian attacks have killed 11 people in Israel, and at least six US service members have been killed.
Early on Saturday, missiles were seen flying towards Israel as the Israeli military said it had identified missiles launched from Iran towards Israel.
Explosions could be heard as Israeli defences activated to shoot down incoming Iranian fire.
Shortly after the barrage, the Israeli army said it had begun a wave of strikes targeting infrastructure in the capital, Tehran.
Israel also attacked neighbouring Lebanon, where it said it was hitting Iranian and Hezbollah targets.
Tehran's Mehrabad Airport was struck, the semi-official Tasnim news agency reported.
Landings resumed at Dubai International Airport, according to aviation-tracking website Flightradar24.
On Friday, Israel said 50 of its warplanes had hit a bunker in Iran still being used by its leadership beneath slain Supreme Leader Ayatollah Ali Khamenei's destroyed Tehran compound.
Israel has expanded the war in Lebanon, pounding Beirut on Friday after ordering an unprecedented evacuation of the capital's entire southern suburbs.
Israel says its bombing in Lebanon aims to root out Hezbollah, the Shi'ite militia that has been a dominant faction in Lebanese politics since the 1980s.
Hezbollah fired on Israel this week to avenge the killing of Khamenei on the war's first day.
About 300,000 people have been displaced in Lebanon in the past four days, according to the Norwegian Refugee Council.
Lebanese authorities reported 123 people killed and 683 wounded as a result of Israeli attacks.
European and US stocks tumbled on Friday, while oil prices hit multi-year highs, with the Strait of Hormuz effectively shut.
About one-fifth of global oil moves daily through the strait.
Washington would provide reinsurance for losses up to $US20 billion ($A28 billion) in the Gulf region to bolster confidence for oil and gas shippers, the US International Development Finance Corp has said.
Russia was providing Iran with locations of US warships and aircraft after Iran's ability to locate US forces was degraded, the Washington Post reported.
Trump also reiterated his demand to have a say in selecting Iran's new supreme leader, a notion rejected by Iravani.
The ambassador said new leadership would be selected "in accordance with our constitutional procedures and solely by the will of the Iranian people".
Iran calls the conflict an unprovoked attack and the killing of Khamenei as an assassination.
Trump on Friday met executives from seven defence contractors, who he said had agreed to accelerate weapons production to replace depleted US supplies.
White House spokeswoman Karoline Leavitt said the US had enough weapons for the Iran campaign, which she said would take about four to six weeks to complete.
