* Price falls offset by optimism despite rising chance of Grexit
* FTSEurofirst 300 down 0.8 pct, EuroStoxx 50 down 1.5 pct
* Banks bear brunt of sell-off, index down 2.8 pct
* Athens bourse shut; U.S.-listed Greek assets sink
* Rolls-Royce slammed after cut to profit outlook (Updates)
By Atul Prakash and Lionel Laurent
LONDON, July 6 (Reuters) - Top euro zone shares fell around 1.5 percent on Monday, a relatively muted reaction to Greek voters' rejection of austerity terms for a financial lifeline.
Banks bore the brunt of the sell-off, with the relevant Euro STOXX index down 3 percent and a raft of Italian banks down 4.4 to 7.5 percent. Southern European lenders have been in the market's sights given their exposure to peripheral euro government debt, whose yields have risen on Greek fears.
With the Athens stock market shut, investors traded Greek assets listed in the United States: National Bank of Greece's U.S. shares were trading around 15.9 percent lower at 1040 GMT while the Global X FTSE Greece 20 ETF (exchange-traded fund) was down around 10.5 percent.
But the overall market fallout was relatively contained. The Eurostoxx 50 index was down 1.5 percent while the broader pan-European FTSEurofirst 300 was down 0.8 percent. European stock-market volatility retreated.
Although several big banks said the risks of a Greek exit from the euro zone had risen since Sunday's "No" vote, investors pointed to the European Central Bank's capacity to limit financial contagion and step in if market turmoil spread.
"The market is, rightly or wrongly, taking a great deal of credence of the fact that the ECB has many more defence mechanisms in place than it did in 2011-12," said Andrew Milligan, head of global strategy at Standard Life Investments.
"Some of the measures we've seen already could be seen as a subtle signal by the ECB that it is ready to step up... This point of the ECB being ready to step in is very important to the market reaction we've seen."
The worst-performing stock on the STOXX Europe 600 index was not even in the eye of the Greek storm. UK aerospace group Rolls Royce lost 9 percent after cutting profit expectations and scrapping a plan to buy back 1 billion pounds ($1.56 billion) of shares halfway through the programme.
With the earnings season set to kick off in the U.S. and an improving economic backdrop in the euro zone, JPMorgan strategists advised clients to cut risk exposure but added that markets would likely be higher on a three-to-six-month horizon.
Some portfolio managers echoed the optimistic outlook.
"We are still positive on Europe with regards to underlying fundamentals. We are positive on earnings and sales growth and are looking for continued earnings surprises," Bill Street, EMEA head of Investment at State Street Global Advisors, said.
"We are still positively exposed to risky assets in the euro zone and see this as a longer-term opportunity to remain invested in Europe." ($1 = 0.6430 pounds) (editing by Jeremy Gaunt)