Public disapproval of the war has been weighing on Trump and his Republican Party ahead of November midterm elections in which they have to defend slim congressional majorities.
A Reuters/Ipsos poll conducted over the weekend showed Trump's approval rating ticking higher to 37%, up three points from last month when it tied the lowest of his presidency.
However, just one in three Americans support the Iran war, the lowest Reuters/Ipsos reading since the conflict's early days, with most saying Trump has failed to explain his goals.
The end of the U.S. campaign after 13 successive nights of intensifying bombing and Trump's remarks on talks sent oil prices tumbling. U.S. crude CLc1 fell 8.21% to $81.98 a barrel, and Brent LCOc1 fell to $87.77 per barrel, down 9.31% on the day.
Trump's decision to suspend U.S. attacks reflected advice from his military that the bombing had reached the limits of what it could achieve, according to a U.S. official and several U.S. media reports.
The U.S. official told Reuters military commanders had advised the president they were running out of targets and that the chairman of the Joint Chiefs of Staff, General Dan Caine, had expressed concern over the depletion of air munitions.
Trump dismissed suggestions that the U.S. faced munitions shortages, saying the military was rapidly rebuilding inventories depleted by shipments to Ukraine. He said he would like more of "the more sophisticated stuff."
Iranian state media outlets cited an "informed source" as saying that Iran had turned around six "offending ships" on Monday that had attempted to cross the Strait of Hormuz without permission.
Trump launched his renewed bombing campaign to punish Iran after Tehran fired on ships using a route promoted by the United States, which told vessels to sail close to the coast of Oman.
Iran says ships may pass only through a Hormuz channel that runs closer to its own coast, which it controls and where it intends to impose transit fees.
The two weeks of renewed U.S. bombing killed scores in Iran and destroyed bridges and tunnels across the south as well as military targets.
Four U.S. service members were killed in return fire against U.S. bases in neighbouring states. Iran also struck civilian infrastructure in Gulf countries, calling it retaliation for U.S. strikes.
It remains unclear what leverage Washington can exert to break Iran's grip on the strait.
Washington and Tehran reached an agreement in June on a framework for talks meant to take place by the end of August to resolve major issues such as Iran's nuclear programme.
But they have disputed the meaning of the memorandum's language about the strait, with Washington insisting it requires Tehran to allow free travel, while Iran says it grants it the authority to supervise transit.