New York's main contract, light sweet crude for January delivery, gained 32 cents to $88.02.
Brent North Sea crude for delivery in February climbed seven cents to $91.67 a barrel in London trade.
The dollar rose slightly against the euro on Friday as positive German economic data failed to offset concerns over the eurozone economy after a huge ratings downgrade for Ireland and more problems in Spain.
A stronger US greenback makes dollar-traded commodities such as oil more expensive for buyers holding rival currencies.
"The ongoing crisis (in Europe) could slow demand," said Phil Flynn of PFG Best.
Signs of improved demand were reinforced by the latest US data showing US crude reserves sank a massive 9.9 million barrels in the week to December 10 -- the biggest weekly drop in eight years.
The United States is the world's biggest oil consumer.
"Buoyed by a positive set of DoE statistics, oil prices consolidated further in their current range," analysts from Barclays Capital said in a report. "The latest weekly data were extremely constructive all around."
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