Trump called off his latest campaign of air strikes after receiving advice from military commanders that the strategy had run its course. The 13 nights of renewed U.S. bombing killed scores in Iran and destroyed bridges and tunnels across the south as well as military targets.
Iran had responded with attacks on U.S. bases in neighbouring countries that killed four service members, and strikes on civil infrastructure in Gulf states that it said were in response to U.S. strikes on civilian targets.
Iran has said it would hold fire as long as Washington does. But drone attacks were reported in Jordan, Saudi Arabia and northern Iran on Monday, and Jordan reported another drone being downed on Tuesday.
Speaking on Monday, Trump expressed optimism for a deal to end the five-month conflict, while warning that U.S. strikes would resume if negotiations failed to deliver.
"I think there's a good chance that something could happen, and if it does, good, if it doesn't, we go back to doing what we were doing two days ago."
Iran says it has not sought any new negotiations with the United States, which it accuses of violating the agreement reached last month on a framework for talks to end the war.
The U.S. president is scheduled to meet Israeli Prime Minister Benjamin Netanyahu in Washington on Tuesday. Although Israel was involved in the initial bombing campaign, it has not been part of subsequent peace talks, and recent relations between the two leaders have been strained.
Trump has had to rein in the Israeli leader from attacking targets in Lebanon to try to weaken Iran-backed Hezbollah militants, complicating peace talks with Tehran.
The end of the U.S. bombing campaign over the weekend sent oil prices tumbling by around 8% on Monday, and the fall continued on Tuesday. Brent crude futures were down more than 2.5% at around $86 a barrel by mid-morning on Tuesday.
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.
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