U.S. West Texas Intermediate (WTI) crude futures rose 89 cents, or 1.3%, to $71.38 a barrel at 0516 GMT, adding to a 35 cent gain from Tuesday.
Brent crude futures climbed 88 cents, or 1.2%, to $75.24 a barrel, after gaining 44 cents on Tuesday.
After coming under pressure on Monday on broad market jitters over the possible default of Chinese property developer China Evergrande Group, the oil market's focus turned to tight supply issues.
"Crude is supported by API weekly report which noted a bigger-than-expected decline in U.S. crude oil stocks," said Ravindra Rao, vice president of commodities at Kotak Securities.
"Prices are still rangebound ahead of EIA weekly report due later today and ahead of U.S. Federal Reserve's monetary policy decision ... In the near term, crude may move with larger markets with focus on China and Fed policy."
U.S. crude stocks fell by 6.1 million barrels for the week ended Sept. 17, market sources said, citing figures from the American Petroleum Institute on Tuesday.
That was a much bigger decline than the 2.4 million-barrel drop in crude inventories that 10 analysts polled by Reuters had expected on average.
The market will be watching for data from the U.S. Energy Information Administration on Wednesday to confirm the big drops in crude and fuel stocks.
"Given the variety of supportive factors in the energy space, notably sky high natural gas prices, which increase oil's appeal as a substitute, and robust physical demand, dips in prices right now are likely to be short-lived," said Jeffrey Halley, analyst at brokerage OANDA.
Global gas prices are expected to break records this winter as a hot northern hemisphere summer leaves inventories low in key markets. read more
Supply is expected to remain tight after Royal Dutch Shell, the largest U.S. Gulf of Mexico producer, said damage to its offshore transfer facilities would cut production into early next year. read more
Further supporting the market, some producers in the Organization of the Petroleum Exporting Countries and their allies, together called OPEC+, are struggling to increase output up to their targeted levels, sources told Reuters. Most of the shortfall is from Nigeria, Angola and Kazakhstan.
