Data from the US Department of Energy showed inventories climbed 2.6 million barrels to 487.4 million in the week ending December 25, confounding forecasts for a drop.
US benchmark West Texas Intermediate (WTI) for delivery in February edged up 15 cents to $36.75 and Brent added 22 cents to $36.68 by around 0800 IST.
Both contracts slumped more than three% on the US data yesterday. WTI has lost 31% and Brent 36% of its value this year. In 2014, WTI lost 46% and Brent 48%.
"Thursday's price rise comes from short-covering and consolidation after the steep decline on Wednesday," said Daniel Ang, an analyst with Phillip Futures in Singapore.
"I think the renewed decline in oil could affect sentiment over energy stocks in Asia today, although we are likely to see very low volumes on the last trading day of the year," said Bernard Aw, market strategist at IG Markets in Singapore.
"I feel we are going to see a very quiet Asia."
Oversupply remains a concern well into 2016 after Organization of the Petroleum Exporting Countries in early December effectively rejected calls to cut its high output levels to revive prices.
Analysts are expecting no let up in production by OPEC and other oil producers such as the United States as they battle for market share.
Iran is also expected to ramp up its oil exports after Western sanctions are lifted next year as part of a deal reached in July to curb Tehran's nuclear programme, further exacerbating the supply and demand imbalance.
Sanjeev Gupta, head of the Asia oil and gas practice at professional services firm EY, said "a host of economic data due from the US, including the closely watched unemployment rate, and China will set the tone for crude oil prices for the first trading week of 2016".