The Israeli military said two barrages of Iranian missiles were launched towards Israel in the first two hours of Wednesday morning. Explosions were heard over Tel Aviv.
Israel told residents in a southwestern area of Tehran to leave so its air force could strike Iranian military installations.
Thousands of people were fleeing the capital and major cities, with heavy traffic congesting roads and some routes suspended, Iranian media reported.
An Israeli military official said 50 fighter jets struck about 20 targets in Tehran overnight, including sites producing raw materials, components and manufacturing systems for missiles, and a facility used to make uranium centrifuges.
The US Office of the Director of National Intelligence says Iran is armed with the largest number of ballistic missiles in the Middle East.
Iran has said its ballistic missiles are an important deterrent and retaliatory force against the US, Israel and other potential regional targets.
Trump warned on social media on Tuesday that US patience was wearing thin.
While he said there was no intention to kill Iranian leader Ayatollah Ali Khamenei "for now", his comments suggested a more aggressive stance towards Iran as he weighs whether to deepen US involvement.
"We know exactly where the so-called 'Supreme Leader' is hiding," he wrote on Truth Social.
"We are not going to take him out (kill!), at least not for now ... Our patience is wearing thin."
Three minutes later Trump posted, "UNCONDITIONAL SURRENDER!"
Trump's sometimes contradictory and cryptic messaging about the conflict between close US ally Israel and longtime foe Iran has deepened the uncertainty surrounding the crisis.
A source said Trump and his team were considering a number of options, including joining Israel on strikes against Iranian nuclear sites.
A White House official said Trump spoke to Israeli Prime Minister Benjamin Netanyahu by phone on Tuesday, and met his National Security Council to discuss the conflict.
The US was deploying more fighter aircraft to the Middle East and extending the deployment of other warplanes, US officials told Reuters.
The US has so far taken only indirect actions in the conflict with Iran, including helping to shoot down missiles fired towards Israel.
Khamenei's main military and security advisers have been killed by Israeli strikes, which constitute the most dangerous security breach targeting Iranian leaders since the 1979 Islamic Revolution.
Ever since Iran-backed Hamas attacked Israel on October 7, 2023, and triggered the Gaza war, Khamenei's regional influence has waned as Israel has pounded Iran's proxies - from Hamas in Gaza to Hezbollah in Lebanon, the Houthis in Yemen and militias in Iraq.
Iran's close ally, Syria's autocratic leader Bashar al-Assad, has been ousted.
Israel launched its air war, its largest ever on Iran, on Friday after saying it had concluded the Islamic Republic was on the verge of developing a nuclear weapon.
Iran denies seeking nuclear weapons and has pointed to its right to nuclear technology for peaceful purposes.
Netanyahu has stressed that he will not back down until Iran's nuclear development is disabled, while Trump says the Israeli assault could end if Iran agrees to strict curbs on enrichment.
The UN nuclear watchdog said on Tuesday an Israeli strike directly hit the underground enrichment halls at the Natanz facility.
Israel says it now has control of Iranian airspace and intends to escalate the campaign in the coming days.
But Israel will struggle to deal a knock-out blow to deeply buried nuclear sites such as Fordow, which is dug beneath a mountain, without the US joining the attack.
Iranian officials have reported 224 deaths, mostly civilians, while Israel said 24 civilians had been killed.
with AP
