Brent crude futures edged up 13 cents to $72.65 a barrel.
"In 2022 there is scope for the 24-member OPEC+ group, led by Saudi Arabia and Russia, to ramp up crude supply by 1.4 million barrels per day (bpd) above its July 2021-March 2022 target," the IEA said.
US West Texas Intermediate futures fell 36 cents, or 0.6%, to $62.79. It had earlier reached $63.48, also the highest since March 18.
The IEA and Organization of the Petroleum Exporting Countries (OPEC) made upward revisions to their global oil demand growth forecasts for 2021 this week to 5.7 million barrels per day (bpd) and 5.95 million bpd respectively.