CORRECTED - CORRECTED-Oil falls under $72, euro zone worries weigh

(Corrects paragraph 12 to ...2130 GMT ..., not 1500 GMT)

* Worries over euro zone fiscal health weigh down market

* Market awaits weekly API oil inventory data due later

* U.S. snowstorm, geopolitical tension offer price support

By Jennifer Tan

SINGAPORE, Feb 9 (Reuters) - Oil sank below $72 a barrel on Tuesday, after rising nearly 1 percent the day before, weighed down by nagging worries over an uncertain demand outlook and the fiscal health of some euro zone countries.

Crude rose on Monday, snapping three sessions of losses, as a weaker U.S. dollar, a cold snap and geopolitical tensions provided support.

But fears over the euro zone's sovereign debt woes continued to cast a pall over commodity and equity markets, with Wall Street closing Monday below the 10,000-level for the first time since November, and Japan's Nikkei average hitting its lowest in two months on Tuesday. [.N] [.T]

Oil prices have lost nearly 10 percent this year, dragged down by data showing bulging fuel stockpiles in the United States despite cold weather, concerns about slower Asian demand if China further tightens its monetary policy, and more recently, jitters over Europe's financial stability.

"There is some unwinding of price increases overnight. The continual flight to quality is underpinning the strength of the U.S. dollar, which is in turn weighing on oil prices and commodities in general," said Ben Westmore, commodities analyst with the National Australia Bank in Melbourne.

"Demand prospects look pretty shaky in the medium term, and all that uncertainty is causing a moderation in equity markets, which is being reflected across commodity markets as well."

U.S. crude for March delivery <CLc1> sank 37 cents to $71.52 a barrel by 0258 GMT, after settling up 70 cents at $71.89 per barrel on Monday.

London Brent crude <LCOc1> fell 25 cents to $69.86.

The euro inched up against the dollar on Tuesday, but remained within sight of an 8-½ month low hit last week, due to concerns over sovereign credit risks in the euro zone. [USD/]

Investors await a special European Union summit on the economy on Thursday as the bloc grapples with a debt crisis in Greece and budget woes in other member states. [ID:nLDE6031IT]

Over the past year, oil prices have frequently weakened as the dollar firmed, at times signalling a flight to safer havens by investors.

The market will also await the release of weekly U.S. oil inventory data from the American Petroleum Institute (API), due at 2130 GMT, for further clues on the recovery in demand from the world's top energy consumer.

A Reuters poll has forecast a mixed report. Domestic crude inventories were seen rising 1.2 million barrels due to increased imports, while distillate stocks, which include heating oil and diesel, were expected to have fallen, and gasoline supplies were likely to have edged higher, the poll showed. [EIA/S]

Some price support will come from another big winter storm expected to sweep across the U.S. mid-Atlantic this week, after a blizzard dumped half a metre of snow over the weekend and closed the federal government. [ID:nN08206421]

U.S. heating demand this week is seen to be 11.5 percent above normal, the National Weather Service said on Monday. [ID:nN08188220]

Rising geopolitical tensions could also underpin oil prices. International pressure for new sanctions against Iran grew on Monday after Tehran announced plans to make higher-enriched uranium and add 10 nuclear sites in a year, reawkening Western fears it wants to develop atom bombs. [ID:nLDE61705I] (Editing by Clarence Fernandez)