* Anticipates stock draws to be greater in H2, 2017
* OPEC compliance 'loosened a touch' in April
* US oil outlook 'improving'
* Global oil demand to continue on 'decelerating trend'
* OECD oil stocks fall for second consecutive month
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The International Energy Agency expects the global oil market's rebalancing to accelerate in the short term, having "almost balanced" in the first quarter as OECD commercial stocks fell for a second consecutive month in March, it said Tuesday in its monthly Oil Market Report.
Related podcast -- Interview: IEA sees oil prices firming if OPEC cuts rollover
But the agency also cautioned that "much work remains to be done" in the second half of 2017 to drain inventories further as the diversity and dynamism of the US shale sector continues to surprise.
OPEC compliance with its output restraint agreement "loosened a touch" in April however, with production rising by 65,000 b/d in April to 31.78 million b/d as increased flows from Nigeria and Saudi Arabia offset lower production from Libya and Iran.
The IEA said OPEC's year-to-date compliance with the production cuts remained robust at 96% but stressed the "need to keep a close eye on Libya and Nigeria where there are signs that production might be rising sustainably."
OPEC and non-OPEC participants will meet on May 25 to review its production agreements, and signs suggest the deal is likely to be extended.
This report was published a day after Saudi Arabia and Russia agreed on the need for a rollover of their output cuts by nine months to March 2018, as the world's top two crude producers step up their commitments to pare back the global oil stock glut.
Overall though, the IEA said that if OPEC's April crude oil production levels of 31.78 million b/d are maintained, and nothing changes elsewhere in the balance that would imply a stock draw of 700,000 b/d.
"Adopting the same scenario approach for the second half of 2017. The stock draws are likely to be even greater. Even if this turns out to be the case, stocks at the end of 2017 might not have fallen to the five-year average, suggesting that much work remains to be done in the second half of 2017 to drain them further," it said.
OECD inventories of crude and oil products fell for a second straight month in March by 32.9 million barrels to 3,025 million barrels, as product stocks fell sharply on lower refinery output and increased exports.
But preliminary data from the IEA suggests oil stocks in the OECD will have risen by 16.2 million barrels in April, "which helps to explain the fall in oil prices seen in the second half of April."
The report also said the call on OPEC crude is expected to rise steadily and reach 33.4 million b/d during the final quarter of the year, implying sharp stock draws if output cuts are extended.
Data also showed OPEC is estimated to have earned more in Q1, 2017 while pumping fewer barrels.
"Supply fell by around 4% versus a record-setting Q4, 2016 while estimated daily revenue was up nearly 5%," it said. "As OPEC turned down the taps from record Q4, 2016 production, the average OPEC basket price of crudes rose from $47.59/b in Q4, 2016 to $52.03/b in Q1, 2017."
Iran saw the most substantial rise, earning an extra $15.2 million a day during Q1 while Saudi Arabia, which is shouldering the bulk of the reduction, made an estimated $12.5 million a day more. Iraq earned an extra $10.5 million a day, according to the report.
Overall global oil supply fell by 140,000 b/d in April to 96.17 million b/d, "as non-OPEC, and especially Canada, pumped less, with production down 90,000 b/d from the same period last year," it said.
Non-OPEC oil production dropped by 255,000 b/d in April, as producers subject to the output cut agreement stepped up compliance and Canadian oil sands output slipped on unscheduled shutdowns.
But non-OPEC output was still 310,000 b/d above year-earlier levels, with renewed growth in the US adding to gains from Brazil, Canada, Kazakhstan and Russia.
However, the agency noted an improving outlook for US crude oil production, which is seen rising by 345,000 b/d from the previous year, and up 790,000 b/d from the end of 2016.
The IEA said US operators have sharply stepped up spending and drilling activity since last year against a backdrop of the coordinated supply cut agreement and higher prices.
It also noted that, alongside production cuts and steady demand growth, a rise in global refinery runs should start to contribute to the rebalancing.
"A major contribution to falling crude stocks in the next few months will be a ramp-up in global crude oil runs. Starting in March, refinery activity is building up and by July global crude throughputs will have increased by 2.7 million b/d," it said.
The IEA maintained its 2017 global oil demand growth forecast at 1.3 million b/d, with demand reaching 97.9 million b/d.
This is despite relative weakness in a number of previously solid countries -- India, the US, Germany and Turkey -- which curtailed the H1, 2017 global demand growth estimate by 115,000 b/d.
The report noted Chinese demand remains relatively strong even as India's demonetization policy continues to cast a long shadow over oil demand, with US demand expected to be flat in 2017.
--Eklavya Gupte, email@example.com
--Edited by Jeremy Lovell, firstname.lastname@example.org