Israeli rescue teams and sniffer dogs combed the rubble of residential buildings destroyed in overnight strikes looking for survivors after at least 10 people, including children, were killed, authorities said.
Iran said at least 138 people had been killed in Israel's onslaught since Friday including 60 on Saturday - half of them children - when a missile brought down a 14-storey apartment block in Tehran.
The Israeli military warned Iranians living near weapons facilities to evacuate on Sunday after Israeli Prime Minister Benjamin Netanyahu and Trump said Israel's attacks would intensify.
An official said Israel had a long list of targets in Iran and declined to say how long the offensive would continue.
Sites attacked on Saturday evening included two "dual-use" fuel sites that supported military and nuclear operations, he said.
Trump, who has lauded Israel's offensive and denied Iranian claims the US has taken part, warned Tehran not to widen its retaliation to include US interests.
"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," he said on Truth Social.
"However, we can easily get a deal done between Iran and Israel, and end this bloody conflict."
The US had been negotiating with Iran to secure a commitment to severely restrict its nuclear program, which Iran says is civilian but Israel sees as an existential threat because of its weapons potential.
Trump gave no details of any possible deal.
Iranian Foreign Minister Abbas Araqchi said Israel's attacks had been aimed at sabotaging those talks, which were due to resume in Oman on Sunday before being cancelled.
He said the offensive had the support of the US and Iran was acting in self-defence.
Israel, which has not signed the global nuclear non-proliferation treaty and is thought to possess nuclear weapons, wants to stop Iran from developing atomic weapons and eliminate its ballistic missile capability.
The International Atomic Energy Agency on Thursday declared Iran in breach of its obligations under the treaty.
Iran said Israel had attacked the Shahran oil depot in the capital but the situation was under control.
The semi-official Tasnim news agency said Israel attacked an oil refinery near the capital on Sunday, and Iran's defence ministry was damaged.
It also reported the arrest of two people accused of belonging to Israel's Mossad intelligence agency in Alborz province.
The latest wave of Iranian attacks on Israel began late on Saturday night, when air raid sirens sent some one million people into bomb shelters in Jerusalem and Haifa.
Residents in Tel Aviv and Jerusalem were told to shelter early on Sunday amid another incoming missile barrage.
The Iran-aligned Houthis, who control most of Yemen, said they had launched ballistic missiles towards Jaffa near Tel Aviv, the first time an ally of Iran has reportedly joined the fray.
Conflict in the Middle East has decimated Tehran's strongest regional proxies - the Hamas militia in Gaza and Hezbollah in Lebanon - reducing its options for retaliation.
Israeli authorities said at least 10 people were killed in overnight missile strikes in northern and central Israel, including three children.
At least six people were killed by an Iranian missile that hit a cluster of residential buildings in the town of Bat Yam.
In the Arab town of Tamra in northern Israel, four women were killed, including a mother and her two daughters.
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