* FTSEurofirst 300 index rises 3.3 percent
* Dexia among most actively traded on rescue plan
* Bank strengthening plan helps support stocks
By Joanne Frearson
LONDON, Oct 5 (Reuters) - European shares rose on Wednesday, snapping three days of losses, after policymakers agreed to strengthen the struggling banking sector and a better-than-expected report on the U.S. service sector boosted optimism about U.S. growth.
Investor confidence improved after European finance ministers agreed to safeguard banks as concerns about a Greek default grew, while German Chancellor Angela Merkel said the government was ready to capitalise its banks if needed.
Dexia rose 1.3 percent in volume more than three-fold its 90-day daily average after France and Belgium prepared a rescue plan for the bank.
The Franco-Belgian bank had dropped as much as 38 percent in the previous session and hit an all time low on worries about its exposure to Greece.
"The market is getting a little more confident that policymakers are more serious about tackling the problems," said Richard Batty, strategist at Standard Life Investments, which has $245 billion of assets under management.
Other banks to feature in the top movers list were French banks Credit Agricole and BNP Paribas , which have exposure to euro zone sovereign debt particularly Italy. They were up 9.9 percent and 8.5 percent respectively.
Credit Agricole had fallen 12.9 percent and BNP Paribas 12.7 percent in the preceding three days on worries that the debt crisis could spark a funding squeeze.
The pan-European FTSEurofirst 300 index closed up 3.3 percent at 916.62 points. It had extended gains in the afternoon following data which showed the U.S. services sector expanded slightly more than expected in September.
The index pushed through a key resistance level -- the 23.6 percent Fibonacci Retracement level of its July to September sell-off at 914.55 points. The next resistance level is seen at the 38.2 percent Fibonacci Retracement or 952.61.
But the index is still in bear market territory and has fallen 23.1 percent since its 2011 high in February on expectations of slowing global growth and fears of contagion in the euro zone debt crisis.
DEBT WORRIES AHEAD
A downgrade of Italian sovereign debt by ratings agency Moody's, although no surprise, highlighted the funding risks facing the euro zone's third biggest economy and vulnerability of the euro zone.
Greece still has to convince inspectors from the IMF, EU and the European Central Banks it can implement reforms before the next aid tranche is released and analysts did not see Wednesday's gains as the start of a long-term bull run.
"We've been through this (market rebound) before. In the end this is the problem: if you recapitalise the banks without addressing the solvency of the sovereign countries, it's a bottomless pit ... How much money is enough? How much recapitalisation is enough?," a London-based bank analyst said.
Batty added although it was "helpful to see a road map" that could give investors a clearer expectation of what might be ahead, he was sceptical until he saw a "concrete plan in place" and remained underweight European equities. (additional reporting by Blaise Robinson) ============================================================ For rolling updates on what is moving European shares please click on ============================================================ For pan-Europeanmarket data and news, click on codes in brackets: European Equities speed guide................... FTSEurofirst 300 index.............................. STOXX Europe index.................................. Top 10 STOXX sectors........................... Top 10 EUROSTOXX sectors...................... Top 10 Eurofirst 300 sectors................... Top 25 European pct gainers....................... Top 25 European pct losers........................
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