(Reuters) - Iranian oil exports have fallen steeply is the past months and could slide further pushing oil prices higher again, the International Energy Agency said on Wednesday, effectively calling on OPEC to maintain current high oil output levels.

The IEA, which advises on energy policies of oil consuming nations, said the world was better supplied with oil now than in recent years but warned against calling it an over-supplied market.

Memories are indeed short: crude prices remain very high in historical terms, and are acting as a drag on household and government budgets in OECD and emerging markets alike, the IEA said in its monthly report.

The report came out as the Organisation of the Petroleum Exporting Countries was due to meet in Vienna this week to discuss production volumes running at a multi-year highs.

Nobody knows exactly how oil supplies will develop this summer, said the IEA, referring to the upcoming embargo by the European Union on Iranian oil and continuing talks between Iran and world powers on Tehran's nuclear program.

The IEA said other bullish factors for oil prices included power sector oil demand this summer and stockpiling by major non-OECD economies including China, which have been accumulating crude in the past months ahead of the Iranian embargo.

It said preliminary data indicated imports of Iranian crude by major consumers had fallen by 1 million barrels per day in April and May from levels seen at the end of last year.

In months ahead, Iran may need to shut in production volumes if export markets remain similarly constrained and storage fills up, the IEA said.

The agency left its global oil demand growth forecast broadly unchanged at 820,000 bpd.

It said its call on OPEC's oil and stocks also remained broadly unchanged although it was 1 million bpd higher for the second half of 2012 at 30.9 million bpd. The figure was still 1 million bpd higher than OPEC's current production levels.

(Reporting by Dmitry Zhdannikov; editing by James Jukwey)