Trump’s announcement came after Iranian state-linked media said Tehran had received a US response to its latest peace proposal.
Iran said the response, delivered via Pakistan, was being reviewed, according to Iran’s semi-official Tasnim news agency.
The US is yet to formally confirm it has replied to Iran. However, Trump reportedly told Israel’s Kan News on Sunday that the proposal was unacceptable to him.
Iranian state media said Tehran’s 14-point peace plan asked for Washington to withdraw its forces from near Iran’s borders and end its naval blockade of Iranian ports, and for all hostilities to cease – including Israel’s offensive in Lebanon.
It also called for an agreement between the two countries to be reached within 30 days.
Iranian state media added that the proposal urged the two warring sides to focus on “ending the war” rather than extending a current ceasefire.
Iranian foreign ministry spokesman Esmaeil Baghaei was quoted by state media as saying that “at this stage, we do not have nuclear negotiations” – a key demand by Washington.
Iran has repeatedly denied it is seeking a nuclear bomb and says its programme is only for peaceful purposes, though the country is the only non-nuclear-armed state to have enriched uranium at near weapons-grade level.
On Saturday, Trump confirmed that Washington had received the latest Iranian peace proposal.
In a post on Truth Social, he wrote that he would review the plan, but that he “can’t imagine that it would be acceptable in that they have not yet paid a big enough price for what they have done to Humanity, and the World, over the last 47 years”.
Speaking to reporters later on Saturday, he said he had been told “about the concept of the deal”, adding: “They’re going to give me the exact wording now.”
Asked by the BBC about whether military strikes against targets inside Iran could be renewed, Trump said it was “a possibility”.
“If they misbehave. If they do something bad,” he said. “But right now we’ll see.”
The US president appeared disinclined to withdraw from the conflict entirely, saying “we’re not leaving” and “we’re going to do it, so nobody has to go back in two years or five years”.
The Iranian state-linked agencies said Tehran’s latest proposal was in response to a nine-point US plan, which envisaged a two-month ceasefire.