Israeli rescue teams combed through the rubble of residential buildings destroyed in overnight strikes using flashlights and sniffer dogs to look for survivors after at least seven people were killed, including children, authorities said.
Tehran has called off nuclear talks that Washington had said were the only way to halt Israel's bombing, while Prime Minister Benjamin Netanyahu said the attacks by Israel so far were nothing compared with what Iran would see in the coming days.
"If we are attacked in any way, shape or form by Iran, the full strength and might of the US Armed Forces will come down on you at levels never seen before," Trump said in a message on Truth Social.
"However, we can easily get a deal done between Iran and Israel, and end this bloody conflict."
Trump gave no details of any possible deal.
Iran has said 78 people were killed there on the first day of Israel's campaign on Friday, and scores more on the second, including 60 when a missile brought down a 14-storey apartment block in Tehran, where 29 of the dead were children.
The Shahran oil depot in Tehran was targeted in an Israeli attack, Iran said, but added the situation was under control.
A fire had erupted after an Israeli attack on an oil refinery near the capital, while Israeli strikes also targeted Iran's defence ministry building, the semi-official Tasnim news agency said on Sunday.
The latest wave of Iranian attacks on Israel began late on Saturday night, sending about a million people into bomb shelters in Jerusalem and Haifa.
The Israeli military warned of another incoming missile barrage in the early hours of Sunday, urging residents to seek shelter.
Explosions echoed through Tel Aviv and Jerusalem as missiles streaked across the skies, with interceptor rockets launched in response.
The military lifted its shelter-in-place advisory almost an hour after issuing the warning.
Yemen's Iran-aligned Houthis said on Sunday they had targeted central Israel's Jaffa with several ballistic missiles, the first time an ally of Iran has joined the fray.
Israel's ambulance service said at least seven people were killed overnight, including a 10-year-old boy, a young girl and a woman in her 20s, and more than 140 were injured in multiple attacks.
Israeli media said at least 35 people were missing after a missile hit an eight-storey building in Bat Yam, south of Tel Aviv.
At least 10 people have been killed in Israel and more than 300 others injured since Iran launched its retaliatory attacks on Friday.
A round of US-Iran nuclear talks due to be held in Oman on Sunday was cancelled, with Iranian Foreign Minister Abbas Araqchi saying the discussions could not take place while Iran was subject to Israel's "barbarous" attacks.
Israel says its operation could last weeks, sparking fears of a regional conflagration dragging in outside powers.
Tehran has warned Israel's allies their military bases in the region will come under fire if they help shoot down Iranian missiles.
However, 20 months of war in Gaza and a conflict in Lebanon in 2024 have decimated Tehran's strongest regional proxies, Hamas in Gaza and Hezbollah in Lebanon.
Israel says its bombardment was designed to avert Iran's last steps to the production of a nuclear weapon.
Tehran insists the program is entirely civilian and that it does not seek an atomic bomb.
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