* IEA says supply up sharply but still geopolitical risks
* Agency raises world oil demand growth forecast slightly
* Iraq, Nigeria and Libya help boost OPEC supply
* OECD industry stocks above five-year average
* Non-OPEC supply growth forecast cut by 90,000 bpd
By Christopher Johnson
LONDON, May 11 (Reuters) - Tension between Iran and the West is likely to keep oil prices high despite a dramatic improvement in world supply and a big build in stocks, the International Energy Agency (IEA) said on Friday.
The agency, which advises 28 industrialised nations on energy policy, said soaring global oil supply from OPEC countries and the United States far outpaced global demand, curbed by poor economic activity in developed nations.
The agency said global oil supply rose 600,000 barrels per day (bpd) to 91 million bpd in April and was now 3.9 million bpd over year ago levels, with 90 percent of the increase coming from OPEC.
Saudi Arabia has said it pumped 10.1 million bpd last month, its highest for more than 30 years, in a bid to meet growing demand and curb oil prices, which hit a three-and-a-half-year high in March.
But the IEA said in its monthly Oil Market Report that uncertainty remained and the agency, which last year released strategic oil stocks to compensate for the outage of Libyan production, would be ready to act if necessary.
"The path of market fundamentals for the rest of the year remains highly uncertain and geopolitical risks will likely continue to keep prices high," the IEA said.
"The IEA will monitor market conditions and stands ready to act if supply conditions warrant it."
The agency kept its forecast for global oil demand growth this year broadly unchanged, raising it by just 20,000 bpd from its previous report to 790,000 bpd.
This would bring global oil consumption this year to around 90 million bpd, it said.
World oil supply was likely to more than match the increase in demand, the IEA said. OPEC oil supply had risen by 410,000 bpd in April, with Iraq, Nigeria and Libya providing 85 percent of the increase, well ahead of demand for OPEC oil.
"OPEC producers have stepped up to the plate and raised supply," David Fyfe, head of the IEA's Oil Industry and Markets division and one of the authors of the report, told Reuters.
North Sea Brent crude futures rose above $128 per barrel in March as investors worried conflict between Iran and the West could cut off oil supplies from the Middle East Gulf.
But prices have fallen sharply over the last two months on the disappointing performance of the European and U.S. economies and as geopolitical tensions have eased. Brent was trading around $111.80 by 1000 GMT on Friday.
"The oil market is still jittery but it is much less uneasy now that supplies and stocks have improved," Fyfe said. "A lot will depend on how much Iranian crude is lost to the market."
The IEA's estimate of demand for OPEC oil for 2012, its 'call on OPEC crude and stock change', was raised by 200,000 bpd to 30.3 million bpd.
At the same time, non-OPEC supply would grow by around 600,000 bpd this year, helping inflate oil inventories.
OECD commercial oil stocks had risen above the five year average for the first time since May 2011, bringing forward demand cover to 60.3 days of consumption, three days above the five year average, the report said.
The IEA's assessment of global oil market conditions is broadly in line with the views of the Organization of the Petroleum Exporting Countries, which said on Thursday it was pumping enough oil to keep world markets more than satisfied.
OPEC also blamed recent high prices on geopolitical risk.
Analysts say higher oil supply should keep pressure on oil prices and inventories will keep rising if OPEC production continues to exceed demand.
"There will be more stock builds this year," said Olivier Jakob, consultant at Petromatrix in Zug, Switzerland. "That's why prices are coming off."