Trump's comments on Friday came hours after Iran's president announced that unnamed countries had begun mediation efforts, briefly raising the possibility, however faint, of a diplomatic resolution a week after the US and Israel launched strikes on Iran.
"There will be no deal with Iran except UNCONDITIONAL SURRENDER!" Trump posted on social media.
"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 regional conflict that has already spilled well beyond Iran's borders, shaken financial markets and sent oil prices soaring.
In response to the attack, Iran has targeted Israel as well as Gulf states that host US military installations.
Inside Israel on Friday, explosions could be heard as Israeli defences activated to shoot down incoming Iranian fire.
The UAE, Kuwait, Qatar, Bahrain and Saudi Arabia also reported fresh drone and missile attacks.
Israel pursued a major expansion of the war in Lebanon, pounding the capital Beirut on Friday after ordering an unprecedented evacuation of the city's entire southern suburbs.
Israel also launched a new attacks on Iran, saying 50 of its warplanes had hit a bunker still being used by Iran's leadership beneath slain supreme leader Ayatollah Ali Khamenei's destroyed Tehran compound.
Israel has extended its bombing to Lebanon to root out Hezbollah, the Shi'ite militia allied to Iran that has been a dominant faction in Lebanese politics since the 1980s.
Hezbollah fired on Israel this week to avenge the death of Khamenei.
About 300,000 people have been displaced in Lebanon in the past four days, according to the Norwegian Refugee Council.
The Israeli military says it has destroyed 80 per cent of Iran's air-defence systems and disabled more than 60 per cent of its missile launchers.
Trump's demand for Iran's surrender, and it likely preventing any quick path to ending the conflict, sent European and US stock indices tumbling.
Oil prices hit their highest prices in years, with the critical shipping lane of the Strait of Hormuz effectively closed down.
Trump told Reuters on Thursday he must have a say in selecting Iran's new supreme leader to replace Khamenei, killed on the war's first day, a demand he repeated on Friday in a remarkable assertion of power over the country of more than 90 million people.
Iran's UN ambassador, Amir Saeid Iravani, told reporters that new leadership would be chosen "in accordance with our constitutional procedures and solely by the will of the Iranian people".
Israel has said openly that it aims to overthrow Iran's ruling system.
Iran has cast the war as an unprovoked attack and describes the killing of Khamenei as an assassination.
Earlier on Friday, Iran President Masoud Pezeshkian posted on social media that "some countries have begun mediation efforts", without giving details.
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 met executives from seven defence contractors on Friday, who he later said had agreed to accelerate weapons production to replace depleted US supplies.
At least 1332 people had been killed in Iran since the US and Israel launched strikes on February 28, according to the Iranian Red Crescent Society.
Lebanese authorities reported 123 people killed by Israeli attacks.
Iranian attacks have killed 11 people in Israel, and at least six US service members have been killed.
