Speaking outside the White House, Trump declined to say whether he had made any decision on whether to join Israel's bombing campaign against Iran.
"I may do it. I may not do it. I mean, nobody knows what I'm going to do," he said.
Trump said Iranian officials had reached out about negotiations including a possible meeting at the White House but "it's very late to be talking," he said.
"Unconditional surrender, that means I've had it."
Asked for his response to Iranian Supreme Leader Ayatollah Ali Khamenei rejecting the idea of surrendering, Trump said: "I say, good luck."
Trump said later on Wednesday in the Oval Office that he has not made a decision on how to proceed on Iran.
He said Iran wants to meet and the US side "may do that".
People jammed highways out of the capital Tehran, a city of 10 million people, as residents sought sanctuary from intensified Israeli air strikes.
In its latest bombing run, Israel said its air force destroyed Iran's police headquarters.
"As we promised - we will continue to strike at symbols of governance and hit the ayatollah regime wherever it may be," Defence Minister Israel Katz said.
Khamenei, 86, rebuked Trump in a recorded speech played on television, his first appearance since Friday.
The United States "should know that any US military intervention will undoubtedly be accompanied by irreparable damage," he said.
"Intelligent people who know Iran, the Iranian nation and its history will never speak to this nation in threatening language because the Iranian nation will not surrender."
Trump has veered from proposing a swift diplomatic end to the five-day-old war to suggesting the United States might join it.
A source familiar with internal discussions said Trump and his team were considering options that included joining Israel in strikes against Iranian nuclear installations.
Defense Secretary Pete Hegseth told a Senate committee that the Pentagon was prepared to execute any order given by Trump.
Israel's military said 50 Israeli jets struck about 20 targets in Tehran overnight, including sites producing raw materials, components and manufacturing systems for missiles.
It advised Iranians to leave parts of Tehran for their own safety while it bombed targets.
Traffic was backed up on highways leading out of Tehran as residents sought sanctuary elsewhere.
Arezou, a 31-year-old Tehran resident, told Reuters by phone that she had made it out to the nearby resort town of Lavasan.
"We will stay here as long as this war continues. My friend's house in Tehran was attacked and her brother was injured. They are civilians," she said.
"Why are we paying the price for the regime's decision to pursue a nuclear program?"
In Israel, sirens rang out warning people of retaliatory Iranian missile strikes.
At Ramat Gan city train station east of Tel Aviv, people were lying on city-supplied mattresses lined along the floor or sitting in the odd camping chair, with plastic water bottles strewn about.
"I feel scared, overwhelmed. Especially because I live in a densely populated area that Iran seems to be targeting, and our city has very old buildings, without shelters and safe spaces," said Tamar Weiss, clutching her four-month-old daughter.
with AP
