* European share gains fade after ECB takes no fresh action
* Draghi Decides not to inject further liquidity into financial system
* Orange jumps on confident guidance
* FTSEurofirst 300 flat, Euro STOXX 50 up 0.3 pct
* Spain and Italy outperform for second day in a row
By Sudip Kar-Gupta and Tricia Wright
LONDON, March 6 (Reuters) - European stock markets gave up their gains on Thursday after the European Central Bank chose not to take action to inject more liquidity into the region's financial system, disappointing some investors.
The FTSEurofirst 300 ended the day flat at 1,344.56 points, having earlier moved higher, while the euro zone's blue-chip Euro STOXX 50 index was up just 0.3 percent at 3,144.53 points, down from its intraday high of 3,158.15 points.
The ECB kept interest rates on hold on Thursday and also chose not to suspend weekly operations in which it soaks up the money it spent on sovereign bonds at the height of the euro zone debt crisis.
Some had expected it would pause this process known as 'sterilisation', which would have added around 175 billion euros ($240.4 billion) in liquidity to the market.
With inflation running in the ECB's "danger zone" below 1 percent - 0.8 percent at the last count - the ECB has discussed ending operations to drain funds from the financial system, a back door way of increasing liquidity.
"Disinflation is still a problem, and the market is a little bit concerned that Draghi does not appear to have changed his stance on that," said Hantec Markets analyst Richard Perry.
The Italian and Spanish stock markets, however, performed better than the broadly flat showing elsewhere in Europe for a second consecutive day.
Italy's FTSE MIB equity index rose by 0.4 percent to 20,838.05 points, having earlier hit its highest level since June 2011, while Spain's IBEX rose 0.9 percent.
The Milan and Madrid markets were helped by gains in Italian and Spanish banks, which have risen on signs of an economic recovery in those countries, which were hit hard by the 2010-2012 euro zone's sovereign debt crisis.
Telecoms operator Orange strongly outperformed the market in brisk trade, rising 10.5 percent and adding the most points to the pan-European FTSEurofirst 300 index.
Orange reassured investors by maintaining its 2014 outlook and its goal of better margins and lower costs which should help stabilise its EBITDA (earnings before interest, tax, depreciation and amortisation).
"The 2014 outlook is bullish on EBITDA stabilisation," analysts at Jefferies wrote in a research note.
Trading volume in Orange came to five times its 90-day daily average, while the FTSEurofirst 300 saw only its regular daily volume.