Brent crude futures rose $1.39, or 1.81%, to $78.23 a barrel by 1333 GMT while U.S. West Texas Intermediate crude (WTI) gained $1.44, or 1.98%, to $74.35, Reuters reported.
Saudi Arabia's energy minister said short-sellers – those betting that prices will fall – should "watch out" for pain.
Some investors took that as a signal that the Organization of Petroleum Exporting Countries (OPEC) and allies including Russia, a group known as OPEC+, could consider further output cuts at a meeting on June 4.
"Oil prices are trading higher ... buoyed by the latest short-seller warning from Saudi Arabia," said OANDA senior market analyst Craig Erlam.
"(But) if past experience is anything to go by, traders may be tempted to call his bluff."
Also boosting oil prices was industry data showing that U.S. crude oil and fuel inventories fell sharply.
Crude inventories fell by about 6.8 million barrels last week, according to market sources citing American Petroleum Institute (API) figures. Gasoline inventories dropped by about 6.4 million barrels.
If data from the Energy Information Administration (EIA), due on Wednesday, confirm these figures, U.S. gasoline inventories would have declined for a third consecutive week to their lowest pre-Memorial Day levels since 2014.
The Memorial Day holiday in the United States, this year on May 29, traditionally marks the beginning of the peak summer travel season in the United States and higher fuel demand.
Weighing on broader markets, another round of debt ceiling talks ended on Tuesday with no signs of progress as the deadline to raise the government's borrowing limit or risk default ticked closer.
Price rises were also capped by news that Britain's stubbornly high inflation rate fell by less than expected last month, according to official data that raised the chances of more interest rate hikes.
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