"They made a proposal, and it's a significant proposal. It's a significant step. It's not good enough," Trump told reporters during an Easter egg event for children on the White House lawn.
"It could end very quickly, the war, if they do what they have to do. They have to do certain things. They know that, they've been negotiating I think in good faith," he said.
Trump later said he thought the Iranian people should rise up against the government in the country if a ceasefire were declared but understood that it was too dangerous for them to do so.
"Well they should do it but, again, the consequences are great," Trump said during a White House news conference.
"I mean, they were told, 'If you protest, you will be shot immediately.'"
Trump, who has threatened to bomb Iran's power plants and bridges, also said he believed Iranians "would be willing to suffer that in order to have freedom".
Trump warned that Iran could be "taken out in one night," as his deadline - 8pm EDT on Tuesday (10am AEST on Wednesday) - for the country to reopen the Strait of Hormuz approached.
"The entire country can be taken out in one night, and that night might be tomorrow night," Trump said.
US officials have been negotiating with Iran indirectly through Pakistan, attempting to get a deal in which Iran will forswear nuclear weapons and reopen the Strait of Hormuz, the oil transit waterway.
Iran said it wanted a permanent end to the war, not just a temporary ceasefire.
A regional official involved in the ceasefire talks says the efforts were continuing.
"We are still talking to both sides," he told the Associated Press, speaking on condition of anonymity to discuss the closed-door diplomacy.
A Pakistani-brokered framework for ending the war emerged from intense overnight contacts and proposes 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 told Reuters on Monday.
Pakistan's army chief, Field Marshal Asim Munir, was in contact "all night long" with US Vice President JD Vance, special envoy Steve Witkoff and Iranian Foreign Minister Abbas Araqchi, the source said.
Iran's foreign ministry spokesman Esmaeil Baghaei said Iran's demands "should not be interpreted as a sign of compromise but rather as a reflection of its confidence in defending its positions".
Trump said on Monday it appeared the latest team representing the Iranian government is "not as radicalised" as others who have been killed in air strikes.
"We think they're actually smarter," he said.
Trump said if it were up to him, the United States would take control of Iran's oil but he said the US public would not back such a move.
"Unfortunately, the American people would like to see us come home. If it were up to me, I take the oil, I'd keep the oil, I would make plenty of money, and I'd also take care of the people of Iran much better than they've been taken care of."
Aerial strikes were reported across the region on Monday, more than five weeks since the US and Israel began pounding Iran in a war that has killed thousands and damaged economies by sending oil prices surging.
Iranian state media said the Revolutionary Guards' intelligence chief Majid Khademi has died.
Israel on Monday claimed responsibility for his death.
Israeli Defence Minister Israel Katz in a statement threatened to destroy Iran's infrastructure and hunt down its leaders "one by one".
Iran said on Monday two of its petrochemical complexes were attacked.
Israeli Prime Minister Benjamin Netanyahu said on Monday that a strike on the petrochemical facility in southern Iran was part of dismantling Iran's Revolutionary Guards "money machine".
"Iran is no longer the same Iran, and Israel is no longer the same Israel. Israel is stronger than ever, and the terrorist regime in Iran is weaker than ever," Netanyahu said.
with AP and DPA
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