* Equities support sentiment but firmer dollar caps market
* 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 detail, prices, comment)
By Christopher Johnson
LONDON, March 23 (Reuters) - Oil steadied below $82 a barrel on Tuesday, supported by stronger stock markets, but 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> was down 1 cent at $81.59 a barrel by 0945 GMT. The April delivery contract expired on Monday, settling up 57 cents at $81.25.
London Brent crude for May <LCOc1> fell 4 cents to $80.50.
"Equity markets are comfortably higher this morning and they are supporting sentiment in all commodities," said Eugen Weinberg, analyst at Commerzbank in Frankfurt.
"But the dollar is stronger, which is a negative factor, as are the fundamentals of supply and demand, which are not good."
European shares rose in early trade on Tuesday with miners higher as gold <XAU=> prices picked up. By 0945 GMT, the FTSEurofirst 300 <
> index of top European shares was up 0.66 percent at 1,072.17 points, after three days of losses.
DOLLAR
Asian shares also rose on Tuesday and edged back towards a two-month peak hit last week, supported by investor expectations for a recovery in the world economy. [
]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.
The strength of the dollar has also helped depress oil as concern over Greece's debt crisis has pushed down the euro. Commodities 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 0.2 percent at 80.805 at 0945 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.
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 expected to have eased by 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 Amanda Cooper)