OPEC agreed in December to cut oil output by 1.8 million bpd until the end of 2018.
"It is not for us to declare on behalf of the Vienna agreement countries that it is 'mission accomplished, ' but if our outlook is accurate, it certainly looks very much like it", the IEA said.
London Brent crude was down 25 cents, or 0.3 per cent, at $71.77 after settling down 4 cents.
"With just under half of global oil supply subject to restraint and oil demand growing steadily, the impact on stocks has been substantial", the agency said. As a result, data released in the "next month or two" could show stockpiles have dropped below the five-year average, said the report.
Oil prices wavered between gains and losses Friday as the International Energy Agency predicted robust oil demand for the full year but warned about risks from disruptions to global trade. The IEA the estimate accounts for a healthy global economy and the 55% increase in crude prices since June. US WTI crude futures were down 12 cents at $66.70.
"Losses from Venezuela helped push OPEC crude output to the lowest level in almost three years and raised (the OPEC cut) compliance to an eye-popping 163%", the IEA said.
Oil-market observers were looking ahead to weekly data Friday from Baker Hughes on the number of rigs drilling for oil in the US, a key metric for activity in the sector.
The IEA left its outlook for non-OPEC growth this year unchanged at 1.8 million b/d, sticking to its view that United States crude production will increase by 1.3 million b/d versus 2017 led by a shale oil recover.
The global oil stocks surplus is close to evaporating, OPEC says.
"This last jump of $5 or so is because of the geopolitical situation caused by the situation in Syria", said Tony Nunan, senior oil risk manager at Mitsubishi in Tokyo. Stockpiles of refined products already have fallen below the five-year average.
Analysts at Tudor, Pickering and Holt said the IEA's latest stock figures imply that the oil market remains 600,000 b/d undersupplied.
USA drillers added seven oil rigs in the week to April 13, bringing the total count to 815, the highest since March 2015, General Electric Co's (GE.N) Baker Hughes energy services firm said in its closely followed report on Friday.
"Looking forward, a healthy global economic forecast for 2018, positive vehicle sales data in recent months, stronger 2018 yea-on-year US product consumption in January and potentially tighter global product markets are expected to boost gasoline and distillates demand ...", OPEC said.