New York's main contract, light sweet crude for delivery in June, rose 53 cents to $111.98 a barrel, while Brent North Sea crude for June gained 38 cents to $124.23.
"The US stock market was up very well yesterday, and we're seeing a rebounding in the oil market (after losses earlier in the week)," said John Vautrain, a Singapore-based analyst at Purvin & Gertz energy consultancy.
Prices were also lifted by hopes of increased demand from Japan as the world's third biggest economy starts to rebuild from last month's devastating quake and tsunami disasters.
"Japan needs more oil to make power in the absence of nuclear power," said Vautrain.
Crude prices had closed higher Wednesday in New York after an unexpected drop in US petroleum reserves and a sharply weaker dollar, which makes dollar-priced commodities cheaper for other currency holders.
The US Department of Energy reported Wednesday that crude oil reserves fell by 2.3 million barrels to 357.0 million barrels in the week ending April 15, contrary to analysts' predictions of a rise after the previous six straight weeks of increases that added nearly 13 million barrels to reserves.
Gasoline stocks fell for a second week running by 1.6 million barrels. And stocks of distillates -- including diesel and heating fuel -- unexpectedly fell, by 148.3 million barrels.
Total petroleum reserves fell by 6.7 million barrels last week in the United States, the world's biggest oil-consumer.