USA crude futures extended gains after the data and was 1.4 per cent, or 68 cents, higher at us$49 a barrel, as of 11:33 a.m. ET.
Brent crude futures for July were up 40 cents at $51.16 a barrel early on Thursday.
In between, the commodity markets are trying to absorb the news that US would pull away from the landmark 2015 global agreement to fight climate change, which was a step that accomplished a major campaign commitment but drew disapproval from USA allies.
"After the fall last week, we should see traders picking up some positions but weak volume and muted movement show the opposite", said Michael McCarthy, a chief analyst at CMC Markets.
Part of the problem for OPEC is booming shale production in the United States.
With Crude Oil down 3.5% below $48 a barrel and Brent Oil 3.43% at just over $50 a barrel, Wednesday was not a good day to be a petro-currency, as the Canadian Dollar and particularly the Norwegian Krone fell across the board in sympathy with their major export.
OPEC and other producers, including Russian Federation, have agreed to restrict output by 1.8 million bpd to drain stockpiles that are close to record highs in many parts of the world.
Oil prices dropped more than 4 percent after the decision as the market had been hoping oil producers could reach a last-minute deal to deepen the cuts or extend them further, until mid-2018.
In other news, on Thursday, crude oil posted a two-sided trade, first rallying after official USA data showed crude inventories fell sharply last week as refining and exports surged to record highs. Crude prices tumbled by about 5% to trade below $49 barrel after the deal was announced.
So far, the production-cut agreement has had little impact on global inventory levels due to rising supply from producers not participating in the accord, such as Libya and Nigeria, and a relentless increase in US shale oil output.
The general trend among U.S. producers points to a need to boost growth forecasts amid anticipated production acceleration the second half of this year, said consultancy Energy Aspects.
Gasoline stocks fell by 2.9 million barrels, compared with analysts' expectations in an economists' poll for a 1.1-million-barrel drop.
Crude exports also hit a peak, rising almost 700,000 bpd to 1.3 million bpd, as imports fell 987,000 bpd, the EIA said.
"That would favor the use and demand of fossil fuels, thus giving a much-needed boost to oil prices", Chanes said.
OPEC, in addition, discussed reducing output by a further 1 to 1.5 percent, and could revisit the proposal should inventories remain high.
Oil markets edged higher on Monday as rising Saudi physical prices and signs of falling OPEC supplies slightly outweighed a persistent rise in United States production. It may also possibly bring about increased output from the USA and tip the Organization of Petroleum Exporting Countries' (OPEC) price securities. American oil explorers, having learned to operate more efficiently during a two-year market slump, have restored nearly all the output lost during the downturn. The country will be added to the Reuters survey from June.The Libyan and Nigerian increases mean OPEC output in May averaged 32.22 million bpd, about 470,000 bpd above its supply target, adjusted to remove Indonesia and not including Equatorial Guinea.The Reuters survey is based on shipping data provided by external sources, Thomson Reuters flows data, and information provided by sources at oil companies, OPEC and consulting firms.