Brent crude rose 87 cents, or 1.2%, to $75.68 by 12:06 p.m. ET (1606 GMT). Its session high, $76.02 after the EIA data, was the highest since October 2018.
"Oil markets are rallying because OPEC is sceptical that the increase in U.S. oil production is going to be enough to change their plans to support prices," said Phil Flynn, senior analyst at Price Futures Group in Chicago.
U.S. investment bank Goldman Sachs said it expects Brent crude prices to reach $80 per barrel this summer as vaccine rollouts boost global economic activity.
The number of Americans filing new claims for unemployment benefits dropped more than expected last week, according to data from the U.S. Labor Department.
The gains appeared to stabilize the market that had slumped from early this month, when prices hit their highest levels this year on expectations for demand recovery.
Two sources from OPEC+ producers said Saudi Arabia would cut output by more than 400,000 barrels per day (bpd) in the next two months on top of its existing cuts.