* Firm U.S. dollar dampens sentiment
* Caution ahead of EU summit on Greek debt crisis
* Coming Up: U.S. Feb home sales (1400 GMT)
* Coming Up: U.S. weekly oil inventory data (2030 GMT) (Updates throughout, changes dateline, pvs SINGAPORE)
LONDON, March 23 (Reuters) - Oil slipped towards $81 a barrel on Tuesday, under pressure as the dollar firmed ahead of a European Union summit to discuss Greece's debt crisis.
The American Petroleum Institute weekly oil inventory report, due later in the day, was expected to 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.
U.S. crude for May delivery <CLc1> slipped 15 cents to $81.45 a barrel by 0845 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 13 cents to $80.41.
"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.
Oil prices have traded above $83 on four occasions this month, but have failed each time to hold the gains, partly due to expectations of an oversupply of oil this year.
World oil demand is still well below its level in 2007, before record prices and global recession slashed consumption.
DOLLAR
The strength of the dollar has also helped depress oil as concerns over Greece's debt crisis have helped pushed down the euro. Commodities such as oil often move inversely to the dollar as they are priced in the U.S. currency on international markets.
The euro held its ground on Tuesday after rebounding from a three-week low against the dollar, helped by gains in stock markets, but still stymied by squabbling over Greece. [
]The dollar index <.DXY>, a measure of its performance against six other currencies, was up 0.15 percent at 80.776 at 0845 GMT, but still well below an eight-month high of 81.342 set in February.
EU leaders will discuss the issue of a financial aid package for 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.
European shares rose in early trade on Tuesday with miners higher as gold <XAU=> prices picked up. By 0845 GMT, the FTSEurofirst 300 <
> index of top European shares was up 0.54 percent at 1,070.88 points, after three days of losses.Asian shares also rose on Tuesday and edged back towards a two-month peak hit last week, supported by investor expectations of a recovery in the world economy. [
]The American Petroleum Institute (API) will unveil its weekly inventory report at 2030 GMT.
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 in January. (Reporting by Christopher Johnson in London and Jennifer Tan in Singapore; editing by Sue Thomas)