* EIA reports big rise in U.S. crude stocks
* Weaker dollar, firmer equities support oil
* Crude at top of range, some see chance of breakout
* Coming Up: U.S. January factory orders due Thursday (Repeating to include link to graphic; updates prices)
NEW YORK, March 3 (Reuters) - Oil rose toward $81 a barrel on Wednesday as a weaker dollar and rising equity markets outweighed a U.S. government report showing a large rise in crude inventories.
U.S. crude stocks rose by 4.1 million barrels, the Energy Information Administration (EIA) said, more than the 1.4 million barrel increase forecast. Gasoline stocks rose 700,000 barrels, slightly more than expected. [
]"The report is not making any difference today because crude is looking at the stock market which is moving up and the weakness in the dollar which is adding more support to the market," said Mike Zarembski, senior commodities analyst at optionsXpress in Chicago.
U.S. crude <CLc1> rose $1.17 at $80.85 a barrel by 1:56 p.m. (1856 GMT), trading as high as $81.23 intraday. In London, Brent crude <LCOc1> gained $1.06 at $79.24. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ For a graphic on crude oil's trading range, click on: http://graphics.thomsonreuters.com/310/OIL_RNGBS0310.gif ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Crude oil is trading within a narrow band of $78 to $80 a barrel, focusing attention on whether the market is likely to break out of that range.
Oil in New York on Tuesday hit a seven-week intraday high of $80.95, within sight of Jan. 11's 15-month high of $83.95.
"Crude oil's charts look fairly constructive," said Edward Meir at MF Global in a report. "Given that we are in shouting distance of the January 2010 highs, we cannot exclude a test of those levels."
The EIA report followed data from industry body the American Petroleum Institute (API) on Tuesday, which showed a 4.1 million-barrel drop in distillate supplies and a 2.7 million barrel rise in crude inventories.
The euro rose against the dollar after Greece pledged $6.5 billion in pay cuts and tax increases to reduce its deficit, easing worries about the country's debt crisis.
A weaker dollar tends to support oil prices, making dollar-denominated commodities cheaper for other currency holders.
Wall Street rose after data on the labor market and the U.S. services sector encouraged investors who had been uncertain about the pace of economic recovery.
The Institute for Supply Management's services gauge rose in February at its fastest pace in more than two years, and the ADP Employment report showed U.S. private employers shed fewer jobs last month, suggesting the labor market may be on the mend.
Oil markets have been monitoring economic data for signs of recovery and a potential rebound in energy demand.
The all-important U.S. nonfarm payrolls data is due on Friday. (Reporting by Alex Lawler in London, Edward McAllister in New York, Alejandro Barbajosa in Singapore; editing by Jim Marshall)