Brent crude was up 67 cents, or 1.5%, at $45.17 a barrel by 1012 GMT, after falling around 1% on Tuesday.
West Texas Intermediate oil was up 65 cents, or 1.6%, at $42.26 a barrel, having dropped 0.8% in the previous session.
The American Petroleum Institute [API] said on Tuesday that crude stocks fell by 4 million barrels last week, versus analysts' expectations in a Reuters poll for a draw of 2.9 million barrels.
It also showed falls in gasoline and distillate stocks. Official government data is due later on Wednesday.
The "fall in U.S. API crude inventories..., the third sizeable weekly fall in a row, has supported prices today," said Jeffrey Halley, senior market analyst at OANDA.
A downward revision to a key U.S. oil production forecast for this year also lent support to prices.
The U.S. Energy Information Administration now expects U.S. crude production to fall by 990,000 barrels per day (bpd) this year to 11.26 million bpd, steeper than the 600,000 bpd decline it forecast last month.
Still, growing uncertainty over a stalemate in Washington in talks for a stimulus package to support recovery from the deepest impact of the pandemic may weigh on prices looking ahead.
In India, refined fuels consumption fell to 15.68 million tonnes in July, down 11.7% year-on-year and 3.5% below June's levels, data from the Petroleum Planning and Analysis Cell (PPAC) of the Ministry of Petroleum & Natural Gas showed.
By Ahmad Ghaddar
