The Organization of the Petroleum Exporting Countries and its allies, a group known as OPEC+, agreed on record output cuts in 2020 to cope with a COVID-induced price crash.
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.
Brent futures rose 20 cents, or 0.3pc, to $63.36 a barrel by 11:43 a.m. EDT (1543 GMT), while U.S. West Texas Intermediate (WTI) crude rose 2 cents to $59.79.
OPEC+ has lowered its oil demand growth forecast for this year by 300,000 barrels per day (bpd), a report from its experts panel meeting seen by Reuters showed.
Ships were moving through the Suez Canal again a day after tugs refloated the Ever Given container carrier, which had blocked the passage for almost a week.
"We would need three months of oil prices sustained at current levels followed by six months of drilling activity before production begins to climb higher on a sustained basis," said Peter McNally at Third Bridge.