* Firm U.S. dollar dampens sentiment
* Caution reigns ahead of EU summit on Greek aid
* Coming Up: U.S. Feb home sales (1400 GMT)
* U.S. weekly oil inventory data (2030 GMT) Updates with prices, dollar, equities)
By Jennifer Tan
SINGAPORE, March 23 (Reuters) - Oil was steady above $81 a barrel on Tuesday, facing pressure from a firmer U.S. dollar and caution ahead of a European Union summit to discuss Greece's debt woes.
The American Petroleum Institute weekly oil inventory report, due later in the day, will offer clues on the outlook for demand in the world's top energy user, while existing February home sales data could shed light on the health of the world's largest economy.
"The market is in a holding pattern, waiting for fresh leads. The biggest issue now is the EU summit later this week, as there is a lot of uncertainty over how the EU will handle the Greece situation," said Informa Global Markets analyst Michelle Kwek in Singapore.
"That is a big risk factor affecting dollar sentiment and by extension, oil as well," said Kwek, adding that oil was likely to trade in a range of $78-$82 a barrel this week.
U.S. crude for May delivery <CLc1> eased 22 cents to $81.38 a barrel by 0615 GMT, after settling at $81.60 a barrel on Monday. The April delivery contract expired on Monday, settling up 57 cents at $81.25 a day earlier.
London Brent crude for May <LCOc1> fell 22 cents to $80.32.
A Reuters poll of 10 oil-tracking analysts and organisations showed the oil market will likely faces oversupply of 150,000 barrels per day (bpd). [
]This month, oil has managed to top $83 four times, but has failed to hold the gains, partly stemming from rising risk aversion due to nagging worries over Greece's debt woes and expectations of oversupply this year.
EU leaders will discuss the issue of a financial aid package for debt-stricken Greece at a summit in Brussels on March 25-26, after Athens said it could not deliver promised deficit cuts if its borrowing costs remained so high, and that it may have to seek help from the International Monetary Fund.
But Germany and its European Union partners clashed on Monday over financial support for Greece, with Chancellor Angela Merkel, who faces fierce domestic opposition to any bailout, continuing to rebuff calls for a euro zone agreement this week. [
]The euro held its ground on Tuesday after rebounding from a three-week low against the dollar, helped by an improvement in risk appetite following gains in U.S. stocks, but still stymied by squabbling over Greece. [
]The dollar index <.DXY>, a measure of its performance against six other currencies, edged 0.13 percent higher to 80.754 at 0615 GMT, but was still well below an eight-month high of 81.342 set in February.
Asian shares rose on Tuesday and edged back towards a two-month peak hit last week, supported by investor expectations of an ongoing recovery in the world economy, and as tech stocks drew support from gains in U.S. peers. [
]At 2030 GMT, the American Petroleum Institute (API) will unveil its weekly inventory report. U.S. crude oil stocks probably rose 1.3 million barrels last week, a preliminary Reuters poll showed. Distillate stocks were seen easing 1.1 million barrels, while gasoline stocks were projected to fall 1.6 million barrels. [
]At 1400 GMT, the National Association of Realtors will release existing U.S. home sales for February. Economists forecast a total of 5.00 million annualised units versus 5.05 million annualised units in January. (Editing by Ed Lane)