"Although the oil market will likely tighten throughout the year, overall non-OPEC production, not just in the U.S., will soon be on the rise again", the IEA said in the report.
The latest US government drilling data showed shale production in May was set to rise to 5.19 million barrels per day (bpd), with output from the Permian play, the largest USA shale region, expected to reach a record 2.36 million bpd.
Last week, the API reported a 1.3-million-barrel draw for crude oil inventories for week ending April 7, while the EIA reported a 2.2-million-barrel draw.
Moreover, oil prices were under pressure as a stronger USA dollar dented investor sentiment, which made the dollar-denominated oil less attractive for holders of other currencies.
Brent crude futures were at $53.34 per barrel at 0715 GMT, up 41 cents, or 0.77 per cent, from their last close.
Opec and several other producers including Russian Federation agreed in December to pump less oil in an orchestrated effort to end an oversupply weighing on prices. On Thursday, before major markets closed for the holiday break, they settled up 3 cents at $55.89 a barrel.
It would be premature to talk about the possible participation of Opec members Iran, Nigeria and Libya in any extension of output limits, Barkindo said in an interview with Bloomberg Television.
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If that is right, May will have the biggest monthly increase since February 2015 and the highest monthly production level since November 2015.
In the week to April 7, for example, refinery runs averaged 91 percent, with throughput rising by 268,000 bpd from the previous week to a respectable 16.7 million barrels per day. Retail sales in the USA fell for a second straight month in March and consumer prices dropped for the first time in just over a year, official data showed on Friday.
China's March gasoline output rose 2.5 percent year-on-year to 11.24 million tonnes, the highest level since at least April 2014, China's National Bureau of Statistics said, adding fuel into an Asian market that is already well supplied.
OPEC and top nonmember producers reportedly will meet May 25 as they remain publicly undecided over whether to extend production cuts.
US supplies of crude are still near records and more than 100 million barrels higher than the five-year average for this time of the year, data compiled from the EIA show.
Then in December, non-OPEC producers led by Russian Federation agreed to cut their own output to 558,000 barrels per day.
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