The agency said crude oil inventories fell by 100,000 barrels in the week to 384.6 million barrels. Stockpiles, however, remain in the upper limit of the average range for this time of year.
Supplies of distillate fuels, which include home heating oil, rose by 2.3 million barrels to 120 million barrels with inventories in the lower limit of the average range.
Stockpiles of gasoline rose by 3.3 million barrels to 203.5 million barrels in the current week.
Inventories of finished gasoline and blending components increased, the agency said.
The EIA said the national average price of regular gasoline fell for the ninth consecutive week with the price dropping 5.7 cents to a national retail average of $3.612 per gallon June 4.
The average price of gasoline came in 16.9 cents under the price from the same week of 2011.