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However, the agency said any production freeze possibly agreed by leading oil producers who are due to meet in Qatar on Sunday would only have a "limited" impact on supplies.
Ahead of the highly anticipated Doha talks, the 29-nation IEA said the oil market, which for months has been depressed by a vast oversupply, was expected to practically balance out in the second half of the year.
Oil prices stuck below $30 on worsening glut fears
Prices shot to 2016 highs this week and are now well over $40 a barrel after plummeting below $30 early in the year. They are nevertheless far below the $100-a-barrel mark of mid-2014.
The IEA said in its monthly oil market report that it still anticipates "steady oil demand growth and falling non-OPEC supply", referring to producers outside of the Organization of the Petroleum Exporting Countries.
"This scenario is now taking shape and the oil market looks set to move close to balance in the second half of this year," it said.
Expectations that the Doha meeting will agree to freeze output have helped buoy prices recently after reports that OPEC kingpin Saudi Arabia and non-OPEC producer Russia had reached a consensus on freezing output, boosting hopes of a wider deal.
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"We cannot know the outcome but if there is to be a production freeze, rather than a cut, the impact on physical oil supplies will be limited," said the IEA, which gives advice to countries on energy policy.
It added: "With Saudi Arabia and Russia already producing at or near record rates and very little upside seen apart from Iran... any deal struck will not materially impact the global supply-demand balance during" the first half of 2016.
Analyst Patrick Dennis, of Oxford Economics, also said he saw a "marginal effect" from the Doha meet.
But he said it "should be seen as a first step towards instilling market discipline, unifying OPEC and eventually bringing Iran back into the fold".
All oil producers, including those in the 13-nation OPEC cartel but also non-cartel members like Russia, which is due to attend the Doha talks, have suffered from the more than 60-percent drop in oil prices since mid-2014.
Falling oil prices - opportunity or threat
The collapse was due to a global glut caused in large part by US shale oil producers flooding the market.
The IEA said it remained confident that in 2016 global oil demand would grow by 1.2 million barrels per day.
India may overtake China as "the main engine of global demand growth", the agency also noted.
On the supply side, the IEA said it saw signs that an expected slide in US shale production "is gathering pace".
"By early April the rig count had fallen nearly 80 percent from the peak seen in October 2014 and more anecdotal evidence is emerging of financial problems taking their toll on the shale pioneers," the IEA said.
The agency said the global oil surplus is expected to fall to 200,000 barrels per day in the second half of 2016, from 1.5 million in the first six months.
While its demand and supply figures are "highly provisional", the agency warned, it added that "there is no doubt as to the direction of travel for the supply/demand balance".
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Meanwhile, the pace of Iran's return to the market after the lifting of sanctions under its nuclear deal with world powers has been "more measured than some expected", the IEA said.
Tehran rejects any output freeze until it regains its pre-sanctions market share and has doubled exports since its nuclear accord took effect in mid-January.
Its March production, at 3.3 million barrels per day, was nearly 400,000 barrels higher than at the start of the year but, while nuclear sanctions have been lifted, some financial ones remain, the IEA added.
Iran has signalled a daily production target of four million barrels, its pre-sanctions level.
World oil prices drifted lower in subdued Thursday morning trade.
Around 1000 GMT, US benchmark West Texas Intermediate (WTI) for delivery in May was down nine cents at $41.67 a barrel. Brent North Sea crude for June delivery fell five cents to $44.13 a barrel compared with Wednesday's close.
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