Oil prices held on to most of the previous session's sharp gains in early trade on Tuesday on uncertainty over the status of ceasefire talks between the United States and Iran and the potential reopening of the ​Strait of Hormuz.

U.S. President Donald Trump said on Monday talks with Iran were ongoing, while Tasnim news agency reported ‌that Tehran had suspended indirect negotiations with Washington.

Brent crude futures inched up 6 cents, or 0.06%, to $95.04 a barrel at 0001 GMT, while U.S. West Texas Intermediate fell 17 cents, or 0.18%, to $91.99 a barrel.

Both benchmarks rose more than 5% in the previous session but pared gains after ​U.S. President Trump said he had not been told that Iran was suspending talks with Washington and that Israel ​had agreed to pull back any troops that were preparing to attack southern Lebanon.

In a separate ⁠interview with CNBC on Monday, Trump had said he did not mind if the talks were over.

Shortly after, Trump issued ​a social media post saying talks with Iran were continuing and told ABC News on Monday that he expects a deal ​to extend the ceasefire and reopen the Strait of Hormuz “over the next week”, according to a post by the outlet on X.

"The market is currently focused on whether there's any concrete progress or setbacks in U.S.-Iran negotiations, the tone and substance of statements from both sides (particularly Iran's threats regarding ​the Strait of Hormuz), and actual physical tanker movements through the waterway," said Tim Waterer, chief market analyst at KCM ​Trade.

The status of the U.S.-Iran negotiations at any given point will ultimately determine whether the current risk premium stays embedded in oil prices ‌or ⁠starts to unwind, Waterer added.

Lebanon on Monday announced a partial ceasefire between Hezbollah and Israel, in what would amount to a limited de-escalation of a conflict that has inflamed the broader war with Iran.

"With headlines continuing to fly out of the Middle East, oil prices are set to remain volatile until clearer evidence of progress towards a peace deal emerges," said Tony Sycamore, market ​analyst at IG.

Iran has effectively ​halted nearly all non-Iranian shipping ⁠into and out of the Gulf since the war began, choking off about a fifth of global oil and liquefied natural gas flows and driving prices up by 50% or more.

U.S. ​crude exports climbed to a record 5.6 million barrels per day in May as the ​Middle East crisis ⁠pushed up demand for the country's oil from Asian and European refiners, ship tracking estimates showed on Monday.

According to a preliminary Reuters poll released on Monday, U.S. crude stockpiles are expected to have fallen by about 3.6 million barrels in the week ended May ⁠29, extending ​the prior week's draw, while distillates and gasoline inventories also are likely ​to have declined.

Shipping executives meeting in Athens on Monday said that any peace deal worked out between the U.S. and Iran would need to offer clear ​rules allowing vessels to resume normal business via the Strait of Hormuz.