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.
The rise in idle primary refining capacity in May was planned mostly due to extension by 34 days of the maintenance period for the CDU-6 unit at Rosneft's Ufa refinery, Refinitiv data showed.
The offline capacity for April has been revised down by 2.5%from the previous plan to 3.37 million tonnes.
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.
Crude inventories fell by 5.9 million barrels in the week to April 9 to 492.4 million barrels, compared with analysts' expectations in a Reuters poll for a 2.9 million-barrel drop.
Oil prices rallied on the report. US crude futures were up $2.50 a barrel, or 4.1%, at $62.68 a barrel, while Brent rose 4% to $66.17 a barrel.
Brent crude was down $1.02, or 1.6%, at $63.96 a barrel by 1334 GMT. West Texas Intermediate US oil was off by $1.16, or 1.9%, at $60.40 barrel.
"The wobble we have seen in prices means that OPEC+ will likely need to take a cautious approach once again," bank ING said. "We are of the view that the group will likely hold output levels unchanged."
The rise in production has followed a slump in February, when Russian oil and gas condensate production declined from 10.16 million in January.
A source familiar with Russia's thinking said on Monday Russia would support broadly stable oil output by OPEC+ group of leading global oil producers in May.