But in a possible sign of progress, the Iranian ambassador to Pakistan said "productive" efforts by Islamabad to mediate an end to the war were "approaching a critical, sensitive stage".
Iran has rejected a US proposal brokered by Pakistan for an immediate ceasefire and the lifting of its effective blockade of the strait, followed by talks on a broader peace settlement within 15 to 20 days, according to a source aware of the plan.
The Iranian response consisted of 10 clauses, including an end to conflicts in the region, a protocol for safe passage through the Strait of Hormuz, lifting of sanctions, and reconstruction, IRNA news agency reported.
On Monday, Trump said "the entire country can be taken out in one night, and that night might be tomorrow night".
He vowed to destroy Iranian power plants and infrastructure if Tehran refused to agree before the deadline.
Without a deal, Trump said "every bridge in Iran will be decimated" by midnight EDT on Wednesday (2pm AEST) and "every power plant in Iran will be out of business, burning, exploding, and never to be used again".
Early on Tuesday, the Israeli military said it had completed a wave of air strikes targeting Iranian government infrastructure in Tehran and other areas.
It was operating air defence systems to intercept missiles launched from Iran.
Israel also issued an advisory urging Iranians to avoid trains and stay away from railways until Tuesday evening.
Saudi Arabia intercepted ballistic missiles towards its eastern region with debris falling near energy facilities, its defence ministry said.
The kingdom has come under attack from hundreds of Iranian missiles and drones since the US and Israel launched the war on Iran on February 28, most of which were intercepted, authorities have said.
Bahrain, Saudi Arabia and the United Arab Emirates issued public safety alerts on Tuesday, while the bridge that connects Saudi Arabia to Bahrain was closed briefly following warning alerts.
With civilian infrastructure under attack across the region, Trump has brushed off questions that his vow to wipe out Iranian power plants would constitute war crimes, saying he was "not at all" concerned about the prospect.
"I hope I don't have to do it," he said.
Iran's envoy to the United Nations said on Monday that Trump's threat to strike was "direct incitement to terrorism and provide clear evidence of intent to commit war crimes under international law".
Iran's deputy sports minister, Alireza Rahimi, called on artists and athletes to form human chains at power plants across the country on Tuesday.
"We will stand hand in hand to say: attacking public infrastructure is a war crime."
Oil prices hovered around $US110 per barrel as Trump's deadline loomed and little visible prospect of the reopening of the Strait of Hormuz, a key global oil transit chokepoint that has spurred inflation worries around the world.
Iran effectively closed Hormuz, which has proved a powerful bargaining chip for Tehran that it is reluctant to relinquish.
Trump was on the verge of a political crisis as Iran proved a tougher adversary than he predicted at the start of the conflict, which he said was aimed at stopping the country building nuclear weapons and developing missiles to deliver them.
With 13 US service members killed since the conflict began, he found himself on an even more perilous ground when a US F-15E fighter jet was downed on Friday and one of the two airmen was left stranded deep inside Iranian territory.
A rescue mission by US commandos to extract the officer to safety helped avert a disastrous escalation of a political crisis for Trump over the war, which has killed thousands of people across the Middle East.
