Brent crude LCOc1 futures were up 19 cents, or 0.4%, at $43.09 a barrel as of 0343 GMT, and U.S. West Texas Intermediate (WTI) crude CLc1 futures rose 17 cents, or 0.4%, to $40.46 a barrel, as reported by Reuters.
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Reflecting a recovery in fuel demand despite the coronavirus pandemic, U.S. crude inventories fell by 8.3 million barrels in the week to July 10, beating analysts' expectations for a decline of 2.1 million barrels, according to data from industry group the American Petroleum Institute.
Official numbers from the U.S. Department of Energy's Energy Information Administration (EIA) are due on Wednesday.
On supply, the market will be closely watching for news from a meeting of the Joint Ministerial Monitoring Committee (JMMC) of the Organization of the Petroleum Exporting Countries (OPEC) later on Wednesday.
Key members of OPEC and allies including Russia, collectively known as OPEC+, are set to decide whether to extend output cuts of 9.7 million barrels per day (bpd) that end in July or ease them to 7.7 million bpd.