"The divergence from the large inventory decline reported by the API makes the report appear more negative than it actually was," said John Kilduff, a partner at Again Capital Management in New York.
Brent crude futures rose 82 cents to $61.02 a barrel by 11:48 a.m. EST (1648 GMT), paring gains from the session high of $61.43. US crude was up 63 cents at $52.28 a barrel, off the session high of $52.88.
Oil prices have fallen by a third since the start of October, when it hit a four-year high above $87. It is set for its biggest quarterly slide since the fourth quarter of 2014.
The market drew support this week after Libya declared force majeure on exports from its largest oilfield on Sunday after tribesmen and state security guards seized the facility.
The Libyan outage followed last week's decision by the Organization of the Petroleum Exporting Countries and some non-OPEC producers including Russia to cut supply by 1.2 million barrels per day (bpd) for six months from Jan. 1.
"The OPEC+ deal from last week will allow more of a bullish position to be taken up by some market participants from this point," analysts at JBC Energy said in a report.
"The crude picture at least looks somewhat firmer for the next six months than it did previously."
Still, a weaker economic outlook and higher production elsewhere have limited price gains. Crude output has surged in the United States, set to end 2018 as the world's top oil producer, ahead of Russia and Saudi Arabia.
"We are quite confident that OPEC+ will be successful in tightening up the front end of the oil market thus keeping the Brent crude oil one-month contract in $60+ a barrel territory over the next six months," SEB commodities strategist Bjarne Schieldrop said.
"Investors and producers however fear a tsunami of additional US shale oil supply in late 2019 and 2020 as new pipelines are installed from the Permian to the US Gulf."