Trump, who has said repeatedly that Iran can never have a nuclear weapon, said on Friday he was not satisfied with the latest Iranian proposal for talks, while Iran's foreign minister said Tehran was ready for diplomacy if the United States changes its approach.
Trump also said on Friday that "on a human basis," he did not prefer the military course of action against Iran and told leaders in the US Congress that he did not need their permission to extend the war beyond a deadline set by law for that day because the ceasefire had "terminated" hostilities.
"Do we want to go and just blast the hell out of them and finish them forever? Or do we want to try and make a deal?" he told reporters at the White House when asked about his options.
Later on Friday, during a speech in Florida, Trump said the United States would not end its confrontation with Iran early, "and then have the problem arise in three more years".
While saying repeatedly he is in no hurry, Trump is under domestic pressure to break Iran's hold on the strait, which has choked off 20 per cent of the world's oil and gas supplies and pushed up US petrol prices.
Trump's Republican Party faces the risk of a voter backlash over higher prices when the country votes in midterm congressional elections in November.
Trump spent Saturday in Florida, at his Mar-a-Lago resort and the Trump National Golf Club in nearby Jupiter.
In the evening, he was due to visit another of his golf resorts, Trump National Doral outside Miami, which is hosting the PGA Cadillac Championship.
The United States and Israel suspended their bombing campaign against Iran four weeks ago, but appear no closer to a deal to end a war that has caused the biggest disruption ever to global energy supplies, roiled global markets and raised worries about the possibility of a wider global economic downturn.
Iran has been blocking nearly all shipping from the Gulf apart from its own for more than two months.
Last month, the US imposed its own blockade of ships from Iranian ports.
Washington has repeatedly said it will not end the war, which has led to the deaths of thousands of people, without a deal that prevents Iran from ever obtaining a nuclear weapon, the primary aim Trump cited when he launched strikes in February in the midst of nuclear talks.
Iran says its nuclear program is peaceful.
Speaking on condition of anonymity to discuss confidential diplomacy, the senior Iranian official said Tehran believed its latest proposal to shelve nuclear talks for a later stage was a significant shift aimed at facilitating an agreement.
Under the proposal, the war would end with a guarantee that Israel and the United States would not attack again.
Iran would open the Strait, and the United States would lift its blockade.
Future talks would then be held on curbs to Iran's nuclear program in return for the lifting of sanctions, with Iran demanding Washington recognise its right to enrich uranium for peaceful purposes, even if it agrees to suspend it.
"Under this framework, negotiations over the more complicated nuclear issue have been moved to the final stage to create a more conducive atmosphere," the official said.
