Benchmark Brent crude fell more than four per cent after the comments from Qatar, extending Monday's steep losses on hopes that an arrangement could soon be reached to restore traffic through the blockaded Strait of Hormuz.
But for now, the strait remained virtually shut, with another ship reportedly coming under attack while trying to cross it.
Trump said on Monday that talks with Iran had started and Iran faced a "last chance" to reach a good deal.
Iranian officials insisted no negotiations with the United States were taking place.
Iran says its only talks are with Oman about the strait, and that no major meetings were planned this week.
But senior US officials struck an optimistic tone on Tuesday, with Treasury Secretary Scott Bessent and Secretary of State Marco Rubio both pointing to progress in discussions aimed at reopening the Strait of Hormuz, a corridor that normally carries about a fifth of global oil and liquefied natural gas shipments.
"There's been progress made in those talks, but not finality yet. We're hoping that will happen very shortly," Rubio told reporters at the US State Department.
Bessent said a deal with Iran on the reopening of Hormuz could be reached by Tuesday or Wednesday.
Qatari foreign ministry spokesman Majed al-Ansari said diplomatic contacts had reached "very progressive stages".
He said mediators including Qatar, Pakistan and Oman were co-ordinating closely to facilitate negotiations and exchange draft proposals between the US and Iran.
A senior Pakistani security official said: "A lot is happening in the background ... We are talking to both sides. Our sole goal at this moment is to make both parties at least agree to start talking."
Trump's comments followed his weekend decision to cancel what he described as "massive attacks" on Iran, extending a pattern in which he has threatened major military action before later backing off and pointing to diplomatic contacts.
Iran has halted most traffic through Hormuz while the US maintains a blockade of Iran-related shipping and ports.
Yemen's Iran-aligned Houthi militia have also imposed a naval blockade on Saudi Arabia in the Red Sea, further restricting oil export routes.
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.
Maritime sources told Reuters on Tuesday that the vessel was a dry bulk ship.
Its crew had to abandon the vessel and one seafarer was missing.
Iran has long demanded control over the strait, which it says it should share with Oman, which controls the opposite shore.
