Inventories at Cushing, the delivery hub for US crude futures, declined more than a million barrels in the week to Aug. 15, traders said citing estimates from energy industry information provider Genscape.
In the latest week to Aug. 11 for which government data was available, Cushing inventories increased nearly 700,000 barrels.
Inventories in the US are closely watched as the market grapples with a global supply glut.
Brent crude was up 50 cents, or 1 percent at $50.77 a barrel by 11:19 a.m. EDT (1519 GMT). US light crude was 20 cents, or 0.4 percent, higher at $46.98 a barrel.
Both benchmarks fell more than 1 percent on Wednesday despite data showing that US inventories last week fell the most in nearly a year.
Energy Information Administration (EIA) data showed commercial US crude stocks have fallen by almost 13 percent from their peaks in March to 466.5 million barrels. Stocks are now lower than in 2016.
US oil output, however, is rising fast as shale producers take advantage of a recent increase in prices.
US crude production rose 79,000 barrels per day (bpd) to over 9.5 million bpd last week, its highest level since July 2015, and 12.8 percent above the most recent low in mid-2016.
"Yesterday, the production number trumped the storage number, but it was still a draw of 9 million," said Bob Yawger, director of energy futures, energy futures at Mizuho. "There are some weaker shorts that are probably sold out and they want to get out."
Rising US output has been undermining efforts by the Organization of the Petroleum Exporting Countries and other producers including Russia to drain a global fuel glut.
They have promised to restrict output by a total of 1.8 million bpd between January this year and March 2018.
William O'Loughlin at Rivkin Securities said that if inventory declines continued at the current pace, US stocks would fall below the five-year average in two months.
"The pace of the declines indicates that OPEC production cuts are having an effect, although the current oil price suggests that the market is sceptical about the longer-term prospects for rebalancing of the oil market," he added.
Brent prices are down almost 12 percent since OPEC and its allies began cutting production in January.