* U.S. crude inventories fall, API says; price rises
* U.S. EIA raises 2010 world oil demand forecast
* Dlr on back foot, commodity currencies shine (Updates prices, adds Asian stocks performance, refiles to add dropped zero in stocks fall figure, 254,000 barrels, in fourth paragraph)
By Fayen Wong
PERTH, Oct 7 (Reuters) - Oil prices rose for the third day and topped $71 a barrel on Wednesday, as an industry report showing a small drawdown in U.S. crude stockpiles last week fed optimism for a recovery in energy demand.
A second day of gains for Asian shares on growing confidence in a strengthening global recovery gave oil prices an extra lift.
U.S. crude for November delivery <CLc1> rose 52 cents to $71.40 a barrel by 0655 GMT, adding to Tuesday's gains of 47 cents. London Brent crude <LCOc1> rose 61 cents to $69.17.
Wednesday's oil gains followed a report by the American Petroleum Institute saying crude stocks fell 254,000 barrels in the week to Oct. 2, defying forecasts for a 2.2-million-barrel increase in a Reuters poll of analysts. [
]Distillate stocks fell 2.9 million barrels, countering expectations for a 300,000-barrel build, while gasoline stocks rose 544,000 barrels, against estimates for a 1.0-million-barrel increase.
The API report is seen as a precursor to the more authoritative data issued by the U.S. Energy Information Administration (EIA), which will be released at 10:30 am EDT (1430 GMT) Wednesday.
The EIA also raised its global oil demand estimate by 170,000 barrels a day for the fourth quarter and said it expected consumption to rise by 1.1 million bpd next year, versus earlier expectations of a 910,00 bpd rise. [
]Over the last two weeks, oil has rebounded from an 11-week low of around $66 in late September back towards the $70-level, but some analysts caution it could lose its footing in the near term.
"Oil looks like it's on shaky ground as we approach the U.S. third quarter reporting season. A lot of near term price gains have been won off a rebounding equity market," said Mark Pervan, a commodities analyst at the Australia & New Zealand Bank.
"I suspect the third-quarter reporting card will struggle to match the impressive second-quarter results, which were mainly driven by one-off aggressive cost cutting."
After having jumped about 40 percent in the second quarter, oil prices have squeezed out a gain of only 1 percent in the September quarter, trading in a band of between $65-$75.
While the global economy is healing from its worst financial crisis since the Great Depression, the economic recovery, along with energy demand, is still fragile, analysts have said.
A U.S. Federal Reserve official said on Tuesday that while the U.S. economy was clearly rebounding, it was too soon to begin to withdraw the Federal Reserve's massive support. [
]Asian shares pushed up about 1.4 percent on Wednesday, with Taiwan's benchmark index nearing a 16-month high, as growing confidence about the global economic outlook boosted resource and financial companies. [
]However, the U.S. dollar was again under pressure, with gold <XAU=> trimming some gains but still hovering near the all-time high of $1,043.45 hit on Tuesday. (Reporting by Fayen Wong; Editing by Michael Urquhart)