"Our conditions are clear, and any move toward reopening the Strait of Hormuz is contingent on these conditions being met," Iranian Foreign Minister Abbas Araghchi posted on social media.
"Only a negotiated solution can get them out of this deadlock."
Iran raised the initiative at the UN General Assembly in New York, saying it had been transmitted to the Americans via Qatari mediators and that it could reopen the strategic waterway and put an end to hostilities in the region within seven days.
But in comments to reporters at the White House on Saturday, Trump said: "I reject their proposal. ... I rejected their deal.
"They want to make a deal to open the Hormuz Strait immediately because they're losing so badly," he said before leaving for Tennessee.
"We're winning tremendously."
Despite Trump's public statements, mediators facilitating Iran's talks with the US have not officially relayed a US rejection of the plan, according to Araghchi.
"We are waiting for the mediators to convey the definitive views to us, and we will make a decision based on them," he posted.
The US has imposed an economic blockade on Iran to put pressure on Tehran to lift its blockade of Hormuz, which has drastically reduced shipping through the strait, even though Trump again asserted the US had control of the waterway.
The Wall Street Journal first reported that Trump had rejected the Iranian proposal, citing unnamed US officials.
It said Trump was privately sceptical that Iran would meet his demands and had told his staff that he sees a renewed bombing campaign as likely after the November US midterm elections to Congress.
A US official had said earlier that discussions with Iran through mediators were "positive and constructive".
The commander-in-chief of Iran's army, Amir Hatam, said the war was at a critical and decisive stage, adding Tehran would not accept a situation in which it was unable to trade while foreign powers used the region's strategic waterways.
"If Iran cannot trade, if Iran cannot live, no one will be able to trade or live," he said, in comments reported by state media.
The Iranians also engaged their Saudi rivals regarding the Strait of Hormuz, underscoring the stakes of a seven-month-old conflict that has disrupted oil flows through a critical shipping lane and taken a toll on the global economy.
Araghchi told reporters at the United Nations on Friday the proposed deal would trigger a seven-day countdown to reopening the strait and a pause in regional fighting.
"If there is seriousness on the US side to come to a deal and reopen the Strait of Hormuz, everything is now prepared," he said.
Iranian President Masoud Pezeshkian, in an interview with the CBS show Face the Nation, said Tehran was ready for talks on its nuclear program and other issues, but would not accept "bullying or coercion".
"Iran is not seeking war, but will defend itself against pressure, threats and attacks," Pezeshkian said, adding that it had already agreed that "we're not supposed to develop nuclear weapons".
Previous attempts at diplomacy have failed to end the war, which began on February 28 with US and Israeli attacks.
It has alternated between pauses and renewed strikes since then, killing thousands while degrading Iran's conventional forces and ailing economy.
Iran and its allies have responded by extending the conflict throughout the region, striking US allies in the Gulf with drones and missiles, while its Houthi allies in Yemen have hit Saudi interests.
Yemen's Houthi-run health ministry said seven people were killed and 40 wounded, including children, in a strike on shops at a market at the Mawiya junction in Taiz province, in the southwest, on Sunday.
Later, Yemen's internationally recognised government said its forces had targeted a Houthi military camp and vehicles at the same junction.
