"We expect the EIA report to display bearish results amidst higher rig counts and production levels in the USA", said Singapore-based brokerage Phillip Futures.
Global benchmark Brent gained $1.11 to settle at $78.23 a barrel.
Brent crude futures, the worldwide benchmark for oil prices, stood at $78.21 per barrel on Tuesday, virtually unchanged from their last close and not far off a three-and-a-half year high of $78.53 a barrel reached the previous session, CNBC reported.
U.S. West Texas Intermediate (WTI) crude futures were at $71.09 a barrel, up 13 cents and also not far off their November 2014 high of $71.89 a barrel reached last week. "Brent is pricing in the idea that all the risk to supplies is overseas - there's a concern that all the supplies that are tight in Europe are only going to get tighter".
The IEA said that the overall market balance was "continuing to tighten", and it lowered its estimate for 2018 global oil demand growth to 1.4 million barrels per day from its previous estimate of 1.5 million.
During the week from April 28 to May 4, the API reported a draw of 1.85 million barrels of crude oil.
US President Donald Trump's decision to reintroduce sanctions on Iran have thrown a curveball into Middle East relations, with many expecting this to have continued ripples throughout the world and region.
A global oil glut has been virtually eliminated, figures published by OPEC showed on Monday, thanks to an OPEC-led pact to cut supplies that has been in place since January 2017 and due to rising global demand.
Additionally, the market retreated as the U.S. Dollar strengthened against other currencies to the highest since December.
In China, the world's biggest oil importer, refinery runs rose almost 12 percent in April compared with the same month a year ago, to around 12.06 million barrels per day (bpd), marking the second-highest level on record on a daily basis, data showed on Tuesday. China's crude oil imports in the first quarter increased by 7 percent on the year to around 9.09 million bpd-a rise of nearly 595,000 bpd on average compared to Q1 2017, according to Reuters calculations.
After the plans for the United States to pull out of the Iran nuclear deal became known, oil prices surged over the uncertainty of what would happen to Iran's oil industry if the U.S. reimposed sanctions, limiting Iran's production.
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