* IEA sees cycle of tightening fundamentals broken for now
* OPEC supply rose in March, hovering near 3-1/2 yr highs
* Sees 2012 world oil demand growth unchanged at 800,000 bpd
By Zaida Espana
LONDON, April 12 (Reuters) - The oil market has broken a two-year cycle of tightening supply conditions, the International Energy Agency (IEA) said on Thursday, as demand softens and Saudi Arabia increases output in response to tensions with Iran.
The agency said in its monthly report that there had potentially been a rise in global oil stocks of 1 million barrels per day (bpd) over the last quarter, and the impact on prices had not yet been fully realised.
"The cycle of repeatedly tightening fundamentals since 2009 has been broken for now," it said.
The IEA, which advises 28 industrialised nations on energy policy, said the possibility that countries, led by the United States, could release stocks from strategic reserves, together with a pledge from top oil producer Saudi Arabia to supply clients ahead of this week's negotiations with Iran over its disputed nuclear programme, had tempered recent price gains.
"Easing first quarter 2012 fundamentals have seen prices recently lose most of the $5 per barrel they gained in March. The muted impact so far is partly because much of this extra supply has been stockpiled on land or at sea," said the IEA.
Brent crude futures rose to highs not seen since 2008 of $128.40 a barrel in early March, but have since given up those gains to trade at around $120.10 on Thursday.
The IEA said it was not surprising that extra barrels were being sent into storage in the typically slacker demand period of March and April, even though the backwardated pricing structure made storing less lucrative.
Analysts said that while the report initially suggests a well supplied market, there remain concerns about replacing Iranian crude.
"At an initial level report appears to present a market that is well supplied ... but if you look closely, concerns around Iran and fact that stocks are still low remain key issues," said Gareth Lewis-Davies, energy commodity strategist at BNP Paribas.
"If you have to replace Iranian oil, we can do that but at the cost of spare capacity. And then, given OECD stocks are low by historical standards, there is less slack in the system."
Inventories in the OECD industrialised nations saw a weaker-than-average draw of 12.4 million barrels in February to 2.63 billion barrels, according to the IEA.
Although stockpiles remain below the five-year average, the smaller draw means the deficit narrowed to 13.9 million barrels from 40.4 million barrels in January.
"It is a moderately bearish report. We don't see much tightness in the market. Inventories have risen, and demand is sluggish," said Samuel Ciszuk, Middle East and North Africa analyst at KBC Energy Economics.
"The IEA sees non-OPEC supply gradually balancing out the recent supply losses. We are basically back to the situation we saw before Libya erupted."
Output from the Organization of the Petroleum Exporting Countries (OPEC) was near a three-and-a-half year high of 31.43 million barrels per day in March, up 135,000 bpd from the previous month.
"I think again the IEA report illustrates that there is plenty of oil in the market at the moment ... There is too much - a physical oversupply," said Commerzbank oil analyst Carsten Fritsch.
Iraq, Libya and the United Arab Emirates increased output in the quarter, while top exporter Saudi Arabia hiked output to around 10 million barrels per day (bpd) in April, up about 100,000 bpd on the month, offsetting losses from Iran and Angola.
Saudi Arabia's oil minister said on Thursday the kingdom would pump more if needed.
Output of 10 million bpd would be the highest since November, when it pumped more than it had for decades to reassure markets.
According to the IEA, Iranian production in March fell by a further 50,000 bpd to 3.3 million bpd, to stand about 250,000 bpd below pre-sanction levels at the end of 2011.
Offtake of Tehran's crude by traditional buyers could drop by between 800,000 and 1 million bpd this summer, the IEA said, citing latest available information.
Production from non-OPEC countries, however, fell in March by 500,000 bpd, led by the UK North Sea and synthetic crude plants in Canada.
For the rest of the year, the agency retained its forecast for oil consumption growth of 800,000 bpd, barely changed from last month's forecast.
"We cannot discount the possibility that prices will remain high so long as geopolitical uncertainties remain," the IEA added.