* FTSEurofirst 300 down 0.1 pct, Euro STOXX 50 down 0.2 pct
* Softened Basel III liquidity requirement boosts banks
* Peugeot up as stake sale report prompts short covering
PARIS, Jan 7 (Reuters) - European shares dipped on Monday, taking a breather from their new year rally, although losses were limited by gains in banking shares propelled by regulators' decision to ease new liquidity rules for the sector.
At 0924 GMT, the FTSEurofirst 300 index of top European shares was down 0.1 percent at 1,165.77, while the UK's FTSE 100 index was down 0.3 percent, Germany's DAX index down 0.4 percent, and France's CAC 40 down 0.4 percent.
The euro zone's blue chip Euro STOXX 50 index was down 0.2 percent at 2,705.22 points.
On Sunday, the Basel Committee of banking supervisors said they will give banks four additional years and more flexibility to build up cash buffers, allowing lenders to put some of their reserves to work, which should boost economic growth.
UniCredit surged 4.2 percent, Societe Generale added 2.5 percent, BNP Paribas gained 2.1 percent, and Barclays rose 3.5 percent.
"Softening Basel requirements is good news for banks, bringing a bit of breathing space which will help the sector continue its recovery," said Lionel Jardin, head of institutional sales at Assya Capital, in Paris.
"Overall, the market's positive trend is still intact, even though the Euro STOXX 50 has already reached a major target around 2,720 points. The market is ripe for a pause, but with so much cash on the sidelines, there are a lot of buyers showing up each time we have a dip."
The STOXX euro zone bank index was up 2.1 percent on Monday. The sector index has jumped 67 percent since late July, when fears of a break-up of the euro zone started to abate following comments from European Central Bank President Mario Draghi about the ECB's determination to do "whatever it takes" to save the currency bloc.
The Euro STOXX 50 has gained 26 percent since then, outperforming a 10 percent rise for Wall Street's S&P 500 over the same period.
JP Morgan Cazenove strategists see Europe's outperformance continuing this year, saying that the region's equities are attractively valued while the United States faces concerns over its fiscal situation.
"We still find widespread scepticism towards the region, the bar is set very low for the potential growth surprise," the strategists wrote in a note.
Peugeot was among the top gainers in Europe on Monday morning, up 9 percent as market speculation that the struggling French carmaker will sell its stake in car parts maker Faurecia fuelled hopes the company could raise as much as 1.5 billion euros, prompting a wave of short covering.
Peugeot is among the most shorted stocks in Europe, with 18 percent of the company's shares out on loan, according to data from Markit. Hedge funds with negative bets on the struggling carmaker are feeling the heat from the stock's 50 percent jump over the past month, forcing some of them to cover their position by buying back the shares.