Global benchmark Brent crude was up 50 cents, or 0.7 percent, at $73.94 a barrel by 0805 GMT, after gaining 0.5 percent on Tuesday.
U.S. light crude was 5 cents higher at $68.57, having risen nearly 1 percent in the previous session.
U.S. crude and fuel stockpiles fell more than expected last week, industry group the American Petroleum Institute (API) reported late on Tuesday.
“The overnight API figures set a positive tone for oil prices with draws across the main inventory categories from crude to a sizeable decline in gasoline, which is seasonally the focal point as the driving season ramps up,” Harry Tchilinguirian, oil strategist for French bank BNP Paribas, told the Reuters Global Oil Forum.
U.S. crude inventories fell by 3.2 million barrels in the week to July 20 to 407.6 million barrels, the API said, compared with analyst expectations for a decrease of 2.3 million barrels.
Crude stocks at the Cushing, Oklahoma, delivery hub fell by 808,000 barrels. Gasoline stocks fell by 4.9 million barrels, compared with analyst expectations in a Reuters poll for a 713,000-barrel drop. [API/S]
Official figures from the U.S. Department of Energy’s Energy Information Administration will be published at 10:30 a.m. EDT (1430 GMT) on Wednesday.
“Prices are moving higher after the API reported a more massive draw than analysts had expected,” said Stephen Innes, trader at brokerage OANDA.
Sentiment was also supported by an International Monetary Fund report about skyrocketing inflation in Venezuela, limiting its ability to boost oil output, Innes said.
“Venezuelan oil production has already plummeted to a new 30-year low of 1.5 million barrels a day in June,” he said.
Oil prices have come under pressure this month as a trade dispute between the United States and China, as well as other major economic blocs, has raised the possibility of slower economic growth and weaker global energy demand as higher tariffs stifle imports.
But the global economy is still growing strongly and it is not clear how the trade dispute may impact business.
Reports that China will increase infrastructure spending have also helped reduce concerns that U.S.-China trade tensions will dent Chinese demand for oil.