A source also told Reuters that seven million barrels is roughly two days' worth of oil imports into Japan, the world's fourth biggest importer.
The bullish inventories report, came a day after crude prices dropped 1%, after EIA raised its near-term outlook for US oil production and revised down its projections for oil prices.
The Organization of the Petroleum Exporting Countries (OPEC) members made a decision to reduce output by 1.8 million barrels per day to rebalance the oil market for the first six months of this year.
"US crude oil production is now solidly above 9.3 million barrels per day with more to come, and refined product, especially for gasoline, is oddly weak", said a partner at hedge fund Again Capital in New York, John Kilduff.
BMI said that "continued output growth. particularly in the US" would cap price upside gains from the supply cuts, adding that it expected average 2017 prices of $57 per barrel for Brent and of $53.75 a barrel for WTI.
For the first four months of 2017, OPEC exports by tanker averaged 25.4 million bpd, down from 26.1 million bpd for the preceding four months.
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Refinery crude runs fell 418,000 bbl/d and utilization rates dropped by 1.8 percentage points to 91.5% of overall capacity, after hitting a record 94.1% three weeks earlier, EIA data showed. Stockpiles probably dropped by 2 MMbbl last week, according to a Bloomberg survey before EIA data Wednesday.
Crude prices had hovered near five-months lows earlier this week, but surged yesterday after the Energy Information Administration released data showing a 5.2 million barrel drop in USA crude stockpiles for the week ended May 5, far exceeding market expectations.
Brent LCOc1 was 30 cents higher at $50.52 a barrel by 0715 GMT.
"U.S. crude oil production is now solidly above 9.3 million barrels per day with more to come, and refined product, especially for gasoline, is oddly weak", John Kilduff, partner at hedge fund Again Capital in NY, told Reuters.
"We should expect healthier markets going forward". "Lower 48 (all states excluding Alaska and Hawaii) oil production is set to expand by an additional 390,000 bpd from May 2017 to December 2017 assuming a WTI price of $50 per barrel".
Saudi Arabia's Energy Minister Khalid al-Falih has already said Riyadh might agree to extending the cuts.
Inventories of U.S. crude fell by 5.25m barrels in the week ended May 5, according to the Energy Information Administration.