Responding to a US proposal through mediator Pakistan, Tehran rejected a ceasefire and said a permanent end to the war was necessary, the official IRNA news agency reported.
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, the agency added.
Trump, who has threatened to rain "hell" on Tehran if it did not make a deal by 8pm Tuesday EDT (10am Wednesday AEST) to open the Strait of Hormuz, a vital route for global energy supplies, rejected the Iranian response and said his deadline was final.
At a news conference, Trump said Iran could be "taken out" in one night "and that night might be tomorrow night" referring to Tuesday EDT.
He vowed to destroy Iranian power plants and bridges, brushing off concerns that such actions would be a war crime or alienate Iran's 93 million people.
Without an agreement with Tehran, Trump said, "every bridge in Iran will be decimated" by midnight (2pm AEST on Wednesday) and "every power plant in Iran will be out of business, burning, exploding, and never to be used again".
Iran's top joint military command in turn said Trump was "delusional" and called Trump's warnings "rude, arrogant rhetoric and baseless threats", according to a statement by spokesperson Ebrahim Zolfaqari on state TV.
After Trump's latest comments, 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," Rahimi said on social media platform X.
Trump said Iranians are "willing to suffer that in order to have freedom" and the US has intercepted messages asking for bombings.
The Pakistani-brokered framework for ending the war proposed an immediate ceasefire, followed by talks on a broader peace settlement to be concluded within 15 to 20 days, a source aware of the proposals said.
Iran also threatened to avenge a US-Israeli attack on Monday on Sharif University of Technology in Tehran, one of the country's top science institutions.
"Aggressors will see our might" in response to the Sharif bombing, Iran's Foreign Minister Abbas Araqchi said on X.
Iran's science minister has accused the United States and Israel of attacking some 30 universities in the war.
At the news conference on Monday, US time, Trump and Secretary of Defence Pete Hegseth praised the successful weekend retrieval from Iran of a US airman whose jet was shot down on Friday.
Hegseth, who has faced scrutiny for outspokenly blending his evangelical religious faith with military operations, described the rescue in explicitly Christian terms, comparing it to the resurrection of Jesus Christ.
Further aerial strikes were reported across Iran on Monday. Hegseth said Monday would have the most strikes since the start of the war, and Tuesday would see even more.
Iranian state media said the Revolutionary Guards' intelligence chief, Majid Khademi, had died. Israel claimed responsibility for his death.
The Israeli military also said it had targeted Iran's air force through a series of strikes on the Bahram, Mehrabad, and Azmayesh airports.
