(Corrects 7th paragraph to say waning not rising risk appetite)
* Euro falls vs dlr after Fitch cuts Greece rating
* German data also weighs; Dubai woes dent risk appetite
* Dollar falls vs yen on dovish Bernanke
By Jessica Mortimer
LONDON, Dec 8 (Reuters) - The euro fell against the dollar on Tuesday, weighed by concerns about Greece's fiscal health after Fitch downgraded the country's credit rating.
Data showing German industrial output unexpectedly fell 1.8 percent month-on-month in October also weighed on the euro, while concerns about Dubai's debt woes pushed investors to seek the safety of the U.S. currency.
Fitch Ratings cut Greece's debt rating to BBB+ from A- with a negative outlook, the first time in 10 years a major ratings agency has put Greece below an A grade, citing fiscal deterioration in the euro zone's weakest member.
The cut followed Standard & Poor's saying in a report that Greek banks faced the highest risks in western Europe.
"While you've got weak data coming out and doubts about Greece and Dubai you will get fickle markets ruled by fear," said James Hughes at CMC Markets.
By 1256 GMT, the euro was down 0.2 percent at $1.4788, while the dollar index gained 0.1 percent to 75.859.
Waning risk appetite also prompted investors to buy the U.S. dollar as European shares fell 1.6 percent, with renewed concerns over exposure to Dubai World weighing on banks.
Worries about Dubai deepened as ratings agency Moody's downgraded six Dubai-linked issuers after concluding that no "meaningful" government support would be provided for top firms like DP World or Emaar Properties.
The dollar stayed weak against the yen, however, falling 1 percent to 88.45 yen, after Federal Reserve Chairman Ben Bernanke on Monday cooled speculation of an early rise in U.S. interest rates.
Bernanke said the U.S. economy still faced headwinds and unemployment could stay high for some time, playing down the impact of Friday's stronger-than-expected jobs report
The U.S. data, which showed fewer jobs were lost in November than expected, had raised some expectations the Fed may start to normalise ultra-easy monetary policy earlier than expected and triggered renewed buying of the dollar which has now faded.
"Bernanke's speech was dovish, and he suggested there would not be an immediate rate rise," said Marcus Hettinger, global currency strategist at Credit Suisse in Zurich.
Analysts said the yen was the main gainer because Friday's jobs data had sparked talk that the yen would return to being the funding currency of choice.
"The yen was the biggest loser after the payrolls data and it is the biggest winner today," Adam Cole, global head of FX strategy at RBC Capital Markets.
The dollar has taken a beating for much of the year on the view that rates in the United States will stay low while those elsewhere rise. This would increase the yield advantage of other currencies against the dollar.
Earlier, European Central Bank President Jean-Claude Trichet said the euro zone faced a bumpy road to recovery.
(Reporting by Jessica Mortimer, editing by Nigel Stephenson)