U.S. West Texas Intermediate (WTI) crude futures rose 78 cents, or 1.23%, to $65.26 a barrel, after gaining 1.4% on Monday.
Brent crude futures rose 86 cents, or 1.27%, to $68.48 a barrel after climbing 1.2% on Monday.
Prices are being supported by the prospect of a pick-up in fuel demand in the United States and Europe, as New York state, New Jersey and Connecticut were set to ease pandemic curbs and the European Union planned to open up to more foreign visitors who have been vaccinated, analysts said.
“This should boost holiday travel to coastal regions, as well as increase mobility in major cities,” ANZ Research analysts said in a note.
For further signs of rising U.S. oil demand, traders will be watching out for reports on crude and product stockpiles from the American Petroleum Institute on Tuesday and the U.S. Energy Information Administration on Wednesday.
Five analysts polled by Reuters estimated on average that U.S. crude inventories fell 2.2 million barrels in the week to April 30. Oil inventories rose in the previous two weeks.
The rate of refinery utilization was expected to have increased by 0.5 percentage points last week, from 85.4% of total capacity in the week ended April 23, according to the poll.
A weaker dollar, hit by an unexpected slowdown in U.S. manufacturing growth, also helped shore up oil prices on Tuesday. The lower dollar makes oil more attractive to buyers holding other currencies.
(Reporting by Sonali Paul; editing by Richard Pullin)