* FTSE 100 up 0.4 pct, CAC 40 up 0.1 pct in shortened trade
* Germany, Switzerland, Italy closed for the day
* Bright economic picture fuels post-Fed rally
* Brisk inflows going into European equities
LONDON, Dec 24 (Reuters) - European stocks edged up on Tuesday morning, adding to a rally in the past four sessions that has helped shares to their best pre-Christmas week since 1999, although trading in the shortened session was thin.
Many stock markets such as Germany, Switzerland and Italy were closed for the Christmas break.
At 0900 GMT, Britain's FTSE 100 index was up 0.4 percent, France's CAC 40 up 0.1 percent, and Spain's IBEX up 0.6 percent.
The euro zone blue chip Euro STOXX 50 was flat, although not all stocks on the index were trading.
For the five days leading up to the Christmas break, it is up 4.5 percent, the best week before the holiday since 1999, Thomson Reuters data showed.
The index is up 16.6 percent in 2013 with just a few sessions remaining before the end of the year, which would be its best performance in four years, mostly propelled by central banks' massive liquidity injections.
However, recent gains have come in a week where the U.S. Federal Reserve has slowed its unprecedented monetary easing, with investors taking heart in stronger economic data and a commitment to lower interest rates for longer.
Late in Monday's session, a survey showed that U.S. consumer sentiment rose to its strongest in five months in December as Americans' outlook on the economy and job prospects improved.
"European markets are extending gains higher after better than expected US economic data released yesterday further reinforces the Fed's stance of curtailing its bond buying programme, boosting market sentiment for risk assets," Kash Kamal, research analyst at Sucden Financial, said.
"Stronger than expected Q3 GDP growth in the US and UK and stable growth in the eurozone... have encouraged investors who were previously on the sidelines to return to equity markets as annual gains across major global indices push to their highest levels since 2009."
Wall Street's Dow Jones industrial average and S&P 500 as well as Germany's DAX trade at all-time highs, other euro zone stock indexes, with the EuroSTOXX 50 0.9 percent off two-year highs.
According to data from fund-tracking EPFR Global, European equity funds have enjoyed net weekly inflows in the past 25 weeks in a row.
In the week ending Dec. 18, even as investors pulled $3.4 billion from global equity funds in the run-up to the U.S. Federal Reserve's decision to start trimming its massive stimulus, investors continued to pour in money into European stocks, EPFR data showed.
After three hours of trading, volumes were extremely low, representing about 9 percent of the daily average on the FTSE 100 and 14.4 percent on the CAC 40.
London's stock market will close at 1230 GMT on Tuesday, while Euronext markets in Paris, Amsterdam, Lisbon and Brussels will close at 1300 GMT. Madrid will also close at 1300 GMT.