New York light crude added 92 cents, or 1.3%, to $70.49. In London, Brent crude climbed 95 cents, or 1.4%, to $71.47.
The US is entering its peak driving season and recent reports have shown that petrol supplies have dipped.
At the same time a number of refineries that had closed for repairs are set to reopen, adding to the demand for oil.
"We're heading into the July 4 holiday, the peak of summer demand, at the same time refineries are coming back on line," said Jason Schenker of Wachovia Bank.
"That's what's holding up this market."
A report by the US Energy Department's Energy Information Administration on Wednesday said gasoline inventories dropped 700,000 barrels in the week ending June 22. Analysts had expected an increase of 1.1 million barrels.
The same report also showed that there was a worsening situation in distillates such as heating oil, adding to the view that more crude will need to be refined.
"The inventory numbers are giving the pattern for the rest of the week," said Kevin Blemkin of Man Financial.