(Repeats to format data at bottom of story)
* FTSEurofirst rises 1.6 pct
* Banks bounce after weakness
* Sainsbury up, Tesco down after results
* Euro zone PMI data highlights weak economic backdrop
By Brian Gorman
LONDON, Oct 5 (Reuters) - European shares rose on Wednesday, led by banks after European finance ministers agreed to safeguard the region's lenders, and as investors snapped up bargains following three days of losses.
Stocks rose across the board, with the STOXX Europe 600 Banking Index up 2.4 percent, though it is still down more than 35 percent in 2011. Heavyweight risers included BNP Paribas and Credit Agricole , both up 6.8 percent.
At 0829 GMT, the FTSEurofirst 300 index of top European shares was up 1.6 percent at 902.24 points, having gone as high as 907.74, after falling 2.7 percent on Tuesday. The index has lost more than 19 percent in 2011.
"This rally may not last. Lots of stocks look cheap. We need a strategy for resolving the sovereign debt crisis in the euro zone. We need s strategy to get on top of the U.S. debt problem," Jeremy Batstone-Carr, strategist at Charles Stanley, said.
"Until we get answers, the market can stay cheap. Economic authorities in Europe have continually failed to come up with a robust policy. Now they're in the last chance saloon."
European finance ministers agreed on Tuesday to safeguard their banks as doubts grew about whether a planned second bailout package for debt-laden Greece would go ahead.
Hours earlier French-Belgian municipal lender Dexia became the first European bank to have to be bailed out due to the euro zone's sovereign debt crisis.
Across Europe, Britain's FTSE 100 , Germany's DAX and France's CAC40 rose between 1.8 and 2.2 percent.
Italy's benchmark rose 1.2 percent, despite Moody's lowering its rating on Italy's bonds by three notches, saying it saw a "material increase" in funding risks for euro zone countries with high levels of debt and warning that further downgrades were possible.
WEAK ECONOMIC BACKDROP
The market maintained gains despite some weak economic data.
The euro zone's private sector contracted for the first time in two years last month, shrinking faster than first reported as new business dried up, while the debt crisis cut expectations for the future to two-year lows, surveys showed.
"The data highlights the damage that the mixed messages and the prevarication are doing to sentiment across the euro zone, with leaders that can't decide on a co-ordinated response to the crisis," Michael Hewson, market analyst at CMC Markets, said.
The STOXX Europe 600 Basic Resources Index rose 3 percent, as copper prices rebounded.
Fortunes contrasted for British supermarkets. J Sainsbury , Britain's No.3 grocer, rose 4.3 percent after posting an expected rise in second-quarter underlying sales, as store extensions and growth in convenience stores, online and non-food ranges helped it to overcome tough trading conditions.
Tesco however fell 0.2 percent after posting one of its biggest-ever falls in underlying sales
French insurer AXA rose 4.7 percent after saying it was fully committed to delivering its mid-term earnings targets and its balance sheet was "robust" despite the market environment.
Later, the ADP jobs report in the United States will give pointers on the strength of the recovery in the world's biggest economy. (Editing by David Holmes)
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