Elsewhere, a religious leader called for "Trump's blood", while Israel said it had begun a "large-scale" attack on Tehran.
Israel announced multiple incoming missile attacks and air sirens sounded in Tel Aviv and Jerusalem.
Iranian state television said additional strikes also targeted US bases.
The Israeli military said it launched targeted attacks in Lebanon at the Iranian-backed Hezbollah militant group and a "large-scale wave of strikes against infrastructure" in Iran's capital, without elaborating.
Explosions were heard in multiple locations in Tehran a short time later.
The US navy sank an Iranian warship on Tuesday night in the Indian Ocean, killing at least 87 Iranian sailors, which Iranian foreign minister Abbas Araghchi decried as "an atrocity at sea".
"Frigate Dena, a guest of India's navy carrying almost 130 sailors, was struck in international waters without warning," he wrote on social media.
"Mark my words: The US will come to bitterly regret (the) precedent it has set."
Ayatollah Abdollah Javadi Amoli, in one of the few clerical statements so far from Iran, said the country was "on the verge of a great test" and called on state television for "the shedding of Zionist blood, the shedding of Trump's blood".
"Fight the oppressive America, his blood is on my shoulders," he said in a rare call for violence from an ayatollah, one of the highest ranks within the clergy of Shiite Islam.
The US and Israel launched the war on Saturday, targeting Iran's leadership, missile arsenal and nuclear program while suggesting that toppling the government is a goal.
But the exact aims and timelines have repeatedly shifted, signalling an open-ended conflict.
President Donald Trump praised the US military on Wednesday for "doing very well on the war front, to put it mildly". Fellow Republicans in the US Senate stood with Trump on Iran as they voted down a resolution seeking to halt the war.
Iran fired on Bahrain, Kuwait and Israel as the conflict spiralled. Turkey said NATO defences intercepted a ballistic missile launched from Iran before it entered Turkey's airspace.
The war has killed more than 1000 people in Iran, more than 70 in Lebanon and around a dozen in Israel, according to officials in those countries.
It has disrupted the supply of the world's oil and gas, snarled international shipping and stranded hundreds of thousands of travellers in the Middle East.
Neighbouring countries braced for potential dangers on Thursday, a day after Iran's paramilitary Revolutionary Guard threatened "the complete destruction of the region's military and economic infrastructure".
Qatar's Interior Ministry said authorities were evacuating residents near the US Embassy in Doha as a temporary precaution, without providing further details.
Fighter jets could be heard overhead in the United Arab Emirates city of Dubai.
And a new attack off the coast of Kuwait appeared to expand the area where commercial shipping was in danger.
An explosion rocked the area early on Thursday, according to the United Kingdom Maritime Trade Operations Centre run by the British military.
It said a tanker apparently came under attack, but the agency did not offer a cause. Iran, in the past, has attacked ships by attaching limpet mines to them.
Prior attacks since fighting began on Saturday have happened in the Gulf of Oman and the Strait of Hormuz, the narrow mouth of the Persian Gulf through which about a fifth of the world's oil is shipped.
Oil prices have soared as Iranian attacks have disrupted traffic through the strait, and global stock markets have been hammered over worries that the spike in oil prices may grind down the world economy.
