* WTI, Brent gain more ground as US output falls
* But global supply glut seen keeping a lid on prices
* Goldman expects prices to trade near $45 a barrel
US West Texas Intermediate (WTI) crude had risen 21 cents, or 0.5 percent, to $44.95 per barrel by 0648 GMT, while benchmark Brent futures gained 20 cents, or 0.4 percent, to $47.51 a barrel.
"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 normalisation 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 US horizontal oil rig count, sustained stock draws or additional Opec production cuts."
The US 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.
There was additional support stemming from a decline in US gasoline inventories.
"Prices were also supported after data showed another strong drawdown in inventories in the US," 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 US summer driving season."
Other analysts and traders noted the US 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.
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.
"Opec compliance with production cuts has been good overall at 104 percent year to date and 106 percent in May, thanks primarily to cuts from Saudi Arabia that have been deeper than their commitment," Jefferies said.
"Despite these efforts the market remains stubbornly oversupplied, with incremental volumes from the US, Libya and Nigeria offsetting much of Opec's efforts."
