UPDATE 2-Oil markets tighten on Saudi cut, China demand-IEA

* Too early to call return to bull market

* Raises sharply world oil demand estimate for 2013

* OPEC supply at lowest for a year, stocks falling (Updates throughout, adding detail, comment)

By Dmitry Zhdannikov and Christopher Johnson

LONDON, Jan 18 (Reuters) - World oil markets are tightening as Chinese fuel demand increases and OPEC supplies fall, draining inventories, the West's energy agency said on Friday, in a trend that could put extra upward pressure on prices.

The International Energy Agency, which advises the industrialised nations on energy policies, has in the past few months described the oil markets as very well supplied.

It said it had now a more "sobering, 'morning after' view" although it was too early to become seriously concerned or declare a return to the bull market.

It steeply raised 2013 global oil demand forecasts despite concerns about the health of the world economy.

"All of a sudden, the market looks tighter than we thought," the IEA said, adding that oil stocks in the developed economies of the Organisation for Economic Co-operation and Development were falling.

"OECD inventories are getting tighter - a clean break from the protracted and often counterseasonal builds that had been a hallmark of 2012."

However, the IEA said that both Chinese demand and Saudi supply were too complex for hasty interpretations.

"The dip in Saudi supply, for one, seems less driven by price considerations than by the weather," it said.

"A dip in air conditioning demand - as well as reduced demand from refineries undergoing seasonal maintenance - likely goes a long way towards explaining reduced output. Nothing for the global market to worry about," the IEA said.

OPEC crude supply in December fell to its lowest level in a year at 30.65 million barrels per day on lower output from Saudi Arabia and Iraq. It said Saudi output fell 290,000 bpd in December to 9.36 million bpd.

Iranian supply stood steady in December at 2.7 million bpd versus November although for the year production plunged by 0.65 million bpd to 3 million bpd.

The IEA raised its call on OPEC crude and stocks for 2013 by 100,000 bpd, to 30 million bpd, still below the current production.

It also said China's recent economic indicators have signalled the potential for a rebound in oil consumption after a slowdown to spectacular growth in 2012.

The IEA said it raised its forecast for global oil consumption in 2013 by 240,000 bpd to 90.8 million bpd, some 930,000 or 1 percent higher that in 2012.

NonOPEC production was projected to rise by 980,000 bpd to 54.3 million bpd, the highest growth rate since 2010.

It said OECD commercial oil inventories fell by 18.7 million barrels in November with winter heating oil stocks looking tight, especially in the Americas.

"The bull market of 20032008 was all about demand growth and perceived supply constraints. The bear market that followed was all about financial meltdown. Today's market, as the latest data underscore, has a lot to do with political risk writ large," it said.

It said that beyond wars and political tensions in Syria, Iran, Iraq, Libya or Venezuela, there were also risks of abrupt tax and trade policy changes in other countries.

"Changes in tax and trade policies, in China as in Russia, can, at the stroke of a pen, shakeup crude and products markets and redraw the oil trade map," it said.

It also added that the kidnapping and murder of foreign workers at the In Amenas gas field has cast a cloud over the outlook for Algeria's energy sector. (Reporting by Dmitry Zhdannikov and Christopher Johnson; editing by William Hardy)