Brent crude rose 29 cents to $64.93 a barrel at 1156 GMT, climbing from an earlier low of $64.43, while U.S. West Texas Intermediate (WTI) futures rose 46 cents to $61.17.
"The ever-expanding US supply continues to pose significant downside risk to oil prices", said Stephen Innes, head of trading for Asia/Pacific at futures brokerage OANDA in Singapore.
Gasoline stocks fell by 6.3 million barrels, compared with analysts' expectations in a poll for a 1.2 million-barrel drop.
With global economic growth strong at 3.8 percent, oil demand will be strong this year, OPEC said, particularly in China.
"Commercial crude stocks in the USA have been recovering and are at their highest level since December 2017".
"Saudi Arabia continues to lead by example by producing below the production targets it agreed to", the energy ministry said in the news release.
The Organization of Petroleum Exporting Countries acknowledged the scale of the shale boom, forecasting for the first time that supply growth from rivals will outstrip the increase in demand this year.More news: Will Harry Kane's injury cost Tottenham their Top 4 spot?
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U.S. crude stocks rose by 5 million barrels, the biggest jump since late January, the U.S. Energy Information Administration (EIA) said.
In theory, this also implies that crude prices are based on extremely shaky numbers as well as sentiment, and one person who is concerned about the effect the price structures will have on fundamentals is Michael Tran, global energy strategist for RBC Capital Markets.
Commerzbank strategist Carsten Fritsch said that "according to the OPEC report, demand for OPEC's oil must be 33 million barrels per day for the rest of the year to get rid of any remaining oversupply". Analysts had forecast a smaller decline of 1.519 million barrels.
Tran told Bloomberg, "we do think over the course of the year oil prices will likely march to the beat of its own drum - so from that perspective we do believe the backdrop for the oil market is actually looking quite constructive".
It expects strong oil demand growth and high OPEC compliance to push inventories further below the five-year average in the third quarter.
"Prices in the upper half of the oil price-band will encourage increased supply as USA production grows and countries reduce compliance with their production quotas", said Terry Marshall, a Moody's Senior Vice President.