* FTSEurofirst 300 down 0.3 pct, Euro STOXX 50 down 0.4 pct
* Softened Basel III liquidity requirement boosts banks
* JPMorgan strategists see Europe stocks outperforming U.S.
* 'No safe-haven among utilities' -Deutsche Bank
* Peugeot up as stake sale report prompts short covering
PARIS, Jan 7 European shares dipped on Monday after hitting a near-two year high early in the day with banking shares rising on the decision by global regulators to ease new liquidity rules for the sector.
The FTSEurofirst 300 index of top European shares was down 0.3 percent at 1,164.04 points, retreating from a near-two year high of 1,167.99 hit earlier in the session.
The euro zone's blue chip Euro STOXX 50 index was down 0.3 percent at 2,700.39 points, after rising to as much as 2,714.18 points, a level not seen since mid-2011.
Despite the day's losses, the two benchmark indexes are up 2.7 percent and 2.4 percent respectively so far in 2013.
"The market's positive trend is still intact, even though the Euro STOXX 50 has already reached a major target around 2,720 points," said Lionel Jardin, head of institutional sales at Assya Capital."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."
After shunning equities during most of the global economic crisis, investors have started to come back to the asset class during the past few months.
According to data from EPFR, global equities enjoyed a sixth straight week of net inflows in the week ended Jan 2, driven by institutional investors.
Although Europe equity funds posted outflows for the first time since the third week of November, Europe funds based in the United States recorded their 21st straight week of inflows.
Banking stocks were in the spotlight on Monday after the Basel Committee of banking supervisors said it 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.
Natixis surged 5.4 percent, UniCredit added 4.4 percent and Banco Popular rose 4 percent.
"The liquidity coverage ratio should be much less penalising for the banks, with a broader range of assets eligible for the calculation of the ratio," said Arnaud Poutier, co-head of IG Markets France.
"This will remove major uncertainties for the banks and the financing of the economy. It's positive for banking stocks, but also for the overall market."
The STOXX euro zone bank index was up 2.1 percent. The sector index has jumped about 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.
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, saying that European stocks still trade at a 40 percent discount on a price-to-book basis compared to U.S. stocks.
According to Thomson Reuters Datastream, the gap between the price-to-book ratio of STOXX 600 Europe shares and Wall Street's S&P 500 is 0.55, well above a 10-year average gap of 0.32.
Shares in large European utilities were among the biggest losers after Deutsche Bank downgraded several firms and warned that there were no safe havens in the sector.
The bank cut its ratings for RWE, E.ON and EDF to "sell" from "hold", with the three stocks falling 1.2-2.5 percent.