U.S. West Texas Intermediate (WTI) crude CLc1 had risen 28 cents, or 0.6 percent, to $44.01 per barrel by 02:15 GMT, while benchmark Brent futures LCOc1 gained 28 cents, or 0.6 percent, to $47.59 a barrel, as reported by Reuters.
"The fast ramp-up in shale drilling and the unexpectedly large rebound in Libya/Nigeria production are on track to slow the 2017 stock draws," investment bank Goldman Sachs said.
"This creates risks that the normalization in inventories will not be achieved by the time the OPEC cut ends next March. We expect this will leave prices trading near $45 (a barrel) until there is evidence of a decline in the U.S. horizontal oil rig count, sustained stock draws or additional OPEC production cuts."
The U.S. Energy Information Administration (EIA) said crude stocks rose 118,000 barrels last week, while weekly production declined 100,000 barrels per day (bpd) to 9.3 million bpd. That was the biggest decline in weekly output since July 2016.
Read alsoOil jumps 1% on weaker dollar, but rise in U.S. drilling drags – mediaThere was additional support stemming from a decline in U.S. gasoline inventories.
"Prices were also supported after data showed another strong drawdown in inventories in the U.S.," ANZ said in a note.
"Gasoline inventories fell 894,000 barrels. This suggests demand is starting to pick up, after a slow start to the U.S. summer driving season."
Other analysts and traders noted the U.S. production decline last week was related to temporary factors like Tropical Storm Cindy in the Gulf of Mexico and maintenance work in Alaska that will likely be reversed in coming weeks.
Futures rose after the EIA report, even though data showed a build instead of the 2.6 million-barrel draw that analysts had forecast in a Reuters poll.
Ian Taylor, head of the world's largest independent oil trader Vitol, said Brent will stay in a range of $40-$55 a barrel for the next few quarters as higher U.S. production slows a rebalancing of the market.
Analysts at JBC Energy in a report saw room for prices to recover, saying "there is now significant room for speculative support for prices to develop if a catalyst were to emerge."
Still, global supplies are ample despite output cuts by the Organization of the Petroleum Exporting Countries (OPEC) and other producing countries of 1.8 million bpd since January.
OPEC and the other producers, trying to reduce a crude glut, agreed in May to extend the supply cut through March 2018. But OPEC has exempted Nigeria and Libya from curbing output.
OPEC delegates have said they will not rush to cut crude output further or end the exemptions, although a meeting in Russia next month is likely to consider further steps to support the market.