Trump has been weighing up whether to attack Iran by striking its well-defended Fordo uranium enrichment facility, which is buried under a mountain and widely considered to be out of reach of all but US "bunker-buster" bombs.
His statement was read out by White House press secretary Karoline Leavitt.
Earlier in the day, Israel's defence minister threatened Iranian Supreme Leader Ayatollah Ali Khamenei after Iranian missiles crashed into a major hospital in southern Israel and hit residential buildings near Tel Aviv, wounding at least 240 people.
Israel's military "has been instructed and knows that in order to achieve all of its goals, this man absolutely should not continue to exist," Defence Minister Israel Katz said.
As rescuers wheeled patients out of the smouldering hospital, Israeli warplanes launched their latest attack on Iran's nuclear program.
Prime Minister Benjamin Netanyahu said he trusted that Trump would "do what's best for America." Speaking from the rubble and shattered glass around the Soroka Medical Centre in Beersheba, he added: "I can tell you that they're already helping a lot."
A new diplomatic initiative appeared to be underway as Iran's Foreign Minister Abbas Araghchi prepared to travel to Geneva for a Friday meeting with counterparts from the United Kingdom, France, Germany and the European Union's top diplomat.
Britain's foreign secretary said he met with US Secretary of State Marco Rubio and envoy Steve Witkoff at the White House to discuss the potential for a deal that could cool the conflict.
"A window now exists within the next two weeks to achieve a diplomatic solution," Britain's David Lammy said in a social media post after Thursday's meeting.
The open conflict between Israel and Iran erupted last Friday with a surprise wave of Israeli airstrikes targeting nuclear and military sites, top generals and nuclear scientists. At least 657 people, including 263 civilians, have been killed in Iran and more than 2,000 wounded, according to a Washington-based Iranian human rights group.
Iran has retaliated by firing 450 missiles and 1,000 drones at Israel, according to Israeli army estimates. Most have been shot down by Israel's air defences, but at least 24 people in Israel have been killed and hundreds wounded.
Israel's Home Front Command asserted that one of the Iranian ballistic missiles fired on Thursday had been rigged with fragmenting cluster munitions. A cluster warhead carries dozens of submunitions that can explode on impact, showering small bomblets around a large area.
At least 80 patients and medical workers were wounded in the strike on Soroka Medical Centre, though much of the hospital building had been evacuated in recent days. Vulnerable patients had been transferred underground.
Iranian officials insisted they had not sought to strike the hospital and claimed the attack hit a facility belonging to the Israeli military's elite technological unit, called C4i.
Israeli airstrikes reached into the city of Rasht on the Caspian Sea early Friday, Iranian media reported. The Israeli military had warned the public to flee the area around Rasht's Industrial City, southwest of the city's downtown. But with Iran's internet shut off to the outside world, it's unclear just how many people could see the message.
Iran's supreme leader has rejected US calls for surrender and warned that any US military involvement would cause "irreparable damage to them."
The International Atomic Energy Agency has said that due to restrictions imposed by Iran on inspectors, the UN nuclear watchdog has lost "continuity of knowledge" about Iran's heavy water production — meaning it could not absolutely verify Tehran's production and stockpile.
