Oil prices rose three per cent after a steep sell-off as investors reassessed optimism over diplomacy, while a cargo vessel reported being struck by an unidentified projectile near the Strait of Hormuz off Oman's coast, according to the UKMTO maritime security agency.
Trump said on Monday that talks with Tehran were under way and Iran faced a "last chance" to reach a deal, while Iranian officials insisted no negotiations with the United States were taking place.
Iran says its only talks are with Oman about the Strait of Hormuz and no major meetings are planned this week.
"They are going on right now," Trump told reporters at an Oval Office event on Monday when asked about negotiations, adding that discussions were taking place at the request of Iran, Saudi Arabia, the United Arab Emirates and Qatar.
"This is a last chance for them (Iran) to sign a good document."
Trump's remarks followed his weekend decision to cancel what he described as "massive attacks" on Iran, repeating a pattern in which he has threatened major military action before stepping back and citing negotiations.
Iran's President Masoud Pezeshkian said Iran did not want the conflict to widen: "We defend our borders, but we do not seek to expand the war," he was quoted as saying by state media.
Iran has halted most traffic through Hormuz while Washington maintains a blockade of Iranian shipping and ports, disrupting a corridor that usually carries about a fifth of global oil and liquefied natural gas shipments.
Maritime sources told Reuters on Tuesday that the vessel struck near Hormuz was a dry bulk ship, and its crew had to abandon the vessel, with one seafarer missing.
Traffic through Hormuz remained slow, with three tankers and three bulk carriers among the six vessels transiting the strait on Monday, down from seven the previous day, Kpler data showed.
In peacetime, more than 100 ships would typically transit a day.
Gulf officials and analysts say Iran is betting it can outlast Washington by turning the region's trade routes, shipping lanes and energy infrastructure into pressure points that steadily raise the cost of confrontation.
In a post on Truth Social on Monday, Trump called Iran's leadership "unbelievably duplicitous", saying they had asked for a meeting and more talks were set for the "immediate future".
Sources in Pakistan, which has been mediating efforts to end the conflict, said attempts to bring Washington and Tehran back to the negotiating table were continuing.
Monday's events appeared to fit a pattern that has emerged since Trump launched "Operation Epic Fury" alongside Israel more than five months ago.
He has repeatedly threatened military action against Iran, only to later point to diplomatic contacts as a reason to step back.
Iran, however, has publicly rejected negotiations with Washington since the collapse in early July of a memorandum of understanding the two sides signed the previous month in an attempt to end the conflict.
Trump has yet to achieve the objectives he set out at the start of the war: dismantling Iran's nuclear programme, curbing its ability to attack regional rivals and creating conditions for Iranians to overthrow their clerical rulers.
The dispute over Hormuz remains a central point of contention.
Washington says the June memorandum required Iran to reopen the strategic waterway, while Tehran says the text explicitly preserved its authority over shipping traffic.
