* MSCI Asia ex-Japan falls 0.4 pct, Nikkei closes up at 33-mth high
* Euro remains bid, dollar loses out
* Data from Asia provide underscore improving global growth outlook
* Demand optimism lifts oil, copper
* European shares likely extend losses
By Chikako Mogi
TOKYO, Jan 31 (Reuters) - Asian shares fell slightly on Thursday after rallies to multi-month highs, and longer for some Southeast Asian markets, while the U.S. Federal Reserve's pledge to retain its stimulus policy undermined the dollar.
Sentiment in Asian markets remained underpinned, however, by positive factory output data in Japan, and strong gross domestic product reports from Taiwan and the Philippines.
A weak dollar and signs of stabilisation in the euro zone underpinned gold, and expectations that demand will pick up for industrial commodities supported oil and copper prices.
European markets are likely to extend losses, with financial spreadbetters predicting London's FTSE 100, Paris's CAC-40 and Frankfurt's DAX would open down as much as 0.3 percent. A 0.1 percent drop in U.S. stock futures suggested a soft open at Wall Street.
After recent gains that took several markets to multimonth highs, investors appeared to adopt a cautious stance ahead of key data such as China's official manufacturing PMI and U.S. monthly nonfarm payrolls on Friday.
Data on Wednesday showing the U.S. economy unexpectedly contracted in the fourth quarter also crimped demand, but traders were quick to note that the underlying fundamentals of the U.S. GDP report were not as bad as the headline number.
"After many years of fears that the (U.S.) economy is going to crash, it seemed like the worst is behind us. So better news out of China and expectations for recovery in the United States caused risk money to come back into equities, commodities and energy," said Tony Nunan, an oil risk manager at Mitsubishi.
Upbeat economic reports from Asia failed to galvanize buying in regional equities, which have sped to multimonth highs, but the data reinforced optimism about the global economic outlook.
Taiwan raised its economic growth forecast for 2013, after the fourth quarter expanded faster than expected and posted its best growth in five quarters on improved demand for the island's electronics exports and stronger consumption.
The Philippines said on Thursday its economy grew 1.5 percent in the December quarter from the previous three months, better than market forecasts.
The MSCI's broadest index of Asia-Pacific shares outside Japan eased 0.4 percent after rising 1.3 percent over the past two sessions to nearly an 18-month high. The index was set for a monthly gain of about 2.5 percent.
Australian shares eased 0.4 percent, pausing after a 10-day winning streak, the longest in more than nine years, which hoisted local shares to 21-month highs.
Southeast Asian stock markets were generally softer but remained near their highs. The Philippines hit a record high for the third day running on Wednesday and Thailand's market surged to a more than 18-year high on Wednesday.
The Federal Reserve on Wednesday kept in place its monthly $85 billion bond-buying stimulus plan, arguing the support was needed to lower unemployment.
The Fed's pledge to support the economy with easy money policies underpinned sentiment, but put the dollar on the defensive.
The dollar languished, easing 0.2 percent to 90.93 yen , off Wednesday's 91.41 yen which was its highest since June 2010. The euro steadied near 123.53 yen, after hitting 123.87 on Wednesday, its peak since May 2010.
A firmer yen weighed on Japan's benchmark Nikkei stock average, but the market managed to wipe out earlier losses to close up 0.2 percent at a fresh 33-month high.
Japan's December factory output rose at the fastest pace in a year and a half and firms expect further gains, raising hopes that stabilising global demand and exports will help pull the economy from its slump.
The euro held near a 14-month high of $1.3588 scaled on Wednesday.
"Euro/dollar we now think will rise to $1.37. The euro crosses are also likely to benefit from the return of exiled capital that left the euro zone," said Gareth Berry, G10 FX strategist for UBS in Singapore.
"Europe is not out of the crisis yet, there is still lots of uncertainty out there, but there has been enough stabilisation to encourage some investors to return," he added.
Reports from the euro zone on Wednesday showed economic sentiment improving more than expected across all sectors in January and a gauge for the phase of the business cycle also rising this month.
Spot gold hovered near its one-week high of $1,683.39 an ounce reached on Wednesday. A weak yen pushed the most active gold contract on the Tokyo Commodity Exchange to a record high of 4,944 yen a gram on Thursday.
U.S. crude futures steadied around $97.96 a barrel and Brent crude was up to a more than three-month high above $115.
Asian credit markets were weighed by the selling in equities, widening the spread on the iTraxx Asia ex-Japan investment-grade index by 5 basis points.