"There will be no deal with Iran except UNCONDITIONAL SURRENDER!" Trump wrote on Friday, US time.
"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."
US Treasury Secretary Scott Bessent said in a television interview the "biggest bombing campaign" of the war was still to come.
Trump had told Reuters in a telephone interview on Thursday he must have a say in selecting Iran's new supreme leader to replace Ayatollah Ali Khamenei, killed on the war's first day.
A White House spokeswoman said consideration was already under way.
"I know there's a number of people that our intelligence agencies and the United States government are looking at," Karoline Leavitt told reporters on Friday.
Iran's UN ambassador, Amir Saeid Iravani, told reporters on Friday the new leadership would be chosen "in accordance with our constitutional procedures and solely by the will of the Iranian people - without any foreign interference".
On the ground, Israel pounded Lebanon's capital Beirut on Friday after ordering an unprecedented evacuation of the entire southern suburbs of the city.
Israel said the targets included a Beirut command centre used by the Iranian Revolutionary Guard's navy unit, along with command centres it said were used by the Hezbollah militant group.
Israel also launched a new wave of attacks on Iran, saying 50 of its warplanes had struck a bunker still being used by Iran's leadership beneath Khamenei's destroyed Tehran compound.
Iran's President Masoud Pezeshkian posted on social media that some countries have begun mediation efforts. He did not identify the nations or provide further details.
"Let's be clear: we are committed to lasting peace in the region, but we have not the slightest hesitation in defending the dignity and authority of our country," he wrote.
About 300,000 people have been displaced in Lebanon in the past four days, according to the Norwegian Refugee Council.
Inside Israel, explosions could be heard as Israeli defences activated to shoot down incoming Iranian fire. The UAE, Kuwait, Qatar, Bahrain and Saudi Arabia all reported fresh drone and missile attacks.
Russia is providing Iran with locations of US warships and aircraft in the Middle East after Iran's ability to locate US forces was degraded, the Washington Post reported, citing three officials familiar with the intelligence.
Meanwhile, Trump met with executives from seven defence contractors on Friday, who agreed to accelerate weapons production, the president said on social media.
At least 1332 people have been killed in Iran since the US and Israel launched strikes on February 28, Iravani said, citing the Iranian Red Crescent Society.
The Lebanese health ministry has reported 123 people killed and 683 wounded as a result of Israeli attacks. Iranian attacks have killed 11 people in Israel since the war started, and at least six US service members have been killed.
And two US officials told Reuters that military investigators believed it was likely American forces were responsible for an apparent strike on an Iranian girls' school that killed scores of children on the first day of the war.
With AP
