The authority said refineries processed crude at an average daily rate of 16 million barrels, unchanged from a week earlier.
An oil pump is seen operating in the Permian Basin near Midland, Texas, U.S. on May 3, 2017.
At 11:22 GMT, May WTI crude oil is trading $57.63, up $0.51 or +0.89% and May Brent crude oil is at $67.14, up $0.56 or +0.85%.
It added that supply cuts this year by the Organization of the Petroleum Exporting Countries (OPEC) and non-affiliated allies like Russian Federation - known as the OPEC+ alliance - aimed at tightening oil markets were also supporting crude prices.
Prices were also supported by US energy services firm Baker Hughes' latest weekly report showing the number of rigs drilling for new oil production in the United States fell by nine to 834. Distillate fuel inventories gained a modest 400,000 barrels, after falling by 2.4 million barrels in the last week of February.
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"On balance, we see a very gradual uptrend for oil this year, with Brent forecast to reach $70 per barrel by the end of the year", NAB said. The EIA also revised down its projected 2020 production figure.
Exports from Venezuela's main oil terminal have been stranded as its worst blackout on record has left parts of the country without power for roughly a week.
Crude rallied this year after the Organisation of the Petroleum Exporting Countries (OEPC) and its allies including Russian Federation, a group known as OPEC+, returned to supply cuts as of January 1. U.S. crude shipments are projected to stand at 8.93 million barrels a day in five years - just 0.59 million less that Riyadh, and 0.24 million barrels more than Moscow.
"I expect to see WTI hitting $60 a barrel in the next couple of weeks as inventories in the USA are impacted by the lack of Venezuelan imports", said Andrew Lipow, president of Lipow Oil Associates in Houston.
Saudi Energy Minister Khalid al-Falih told Reuters two days ago that it would be too early to change a production curb pact agreed by the Organisation of Petroleum Exporting Countries (OPEC) and its allies, which includes Russian Federation, another major producer, before June.