* Europe shares dip as Greece summit awaited
* China shares drop despite support measures
* Oil up after falling 6 percent on Monday
* Wall Street looks set for gains
By Nigel Stephenson
LONDON, July 7 (Reuters) - European stocks fell and the euro hit a five-week low against the dollar on Tuesday before a euro zone summit to discuss the Greek debt crisis, while a fall in Chinese shares reminded investors of other clouds on the horizon.
Oil recovered some ground after a selloff on Monday prompted by Greek rejection of the terms of a bailout and the Chinese stock market turmoil.
However, U.S. shares looked set to open higher, according to stock index futures ESc1 SPc1 .
Euro zone finance ministers met in Brussels and the bloc's leaders will meet later in the day. They are waiting for proposals from Greek Prime Minister Alexis Tsipras as his country's banks rapidly run out of cash. Failure to reach a deal would make it more likely Greece will drop out of the euro.
The Euro STOXX 50 index of euro zone blue-chip shares .ESTOXX50E fell 0.9 percent after opening in positive territory. The index fell 2.2 percent on Monday after Greece voted against accepting the terms of a rescue deal on Sunday.
Germany's DAX index .GDAXI lost 0.6 percent while Italy's FTSE MIB .FTMIB edged down 0.3 percent.
"We're surprised with how little markets have sold off following the referendum, but there seems to be faith in the 'Draghi put', and peripheral markets have decoupled from Greece," said James Butterfill, global equity strategist at Coutts.
"Markets may well tread water until we get some sort of decision from the European summit."
German 10-year yields DE10YT=TWEB fell 10 basis points to 0.67 percent. However, yields on government bonds from Italy, Spain and Portugal, the countries considered most vulnerable to contagion from Greece, also fell. On Monday, they rose.
Italian 10-year yields IT10YT=TWEB were down 6 bps at 2.31 percent.
"The markets appear quite remarkably confident on a deal being reached," said Lyn Graham-Taylor, a strategist at Rabobank.
German Bund futures opened sharply higher after the European Central Bank raised on Monday the discount it charges on collateral that Greek banks must offer in exchange for funds. Sources said the move was largely symbolic, since the amount Greek banks can borrow is capped.
The fall in German yields helped push the euro EUR= down 0.7 percent to $1.0972 and 0.8 percent lower against the yen EURJPY= . The dollar rose 0.6 percent against a basket of currencies .DXY .
Many asset managers believe a Greek exit from the euro can still be avoided. Others say the ECB will step in to limit contagion. ID:nL8N0ZM2DM
"It is a drift lower for the euro, with things likely to get interesting if it drops below $1.0970," said Jeremy Stretch, head of currency strategy at CIBC World Markets. "The markets are reasonably relaxed at this stage because they believe the ECB will step in to take action to contain any contagion, should Greece step out of the union."
CHINA FALLING
Earlier, Asian shares drooped after further losses in China, despite measures the authorities put in place at the weekend to halt a slide of almost 30 percent since mid-June.
China's CSI 300 .CSI300 index of the biggest listed companies in Shanghai and Shenzhen closed down 1.8 percent. It had fallen more than 5 percent earlier in the day.
MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS fell 0.7 percent, though Japan's Nikkei .N225 rose 1.3 percent after a sharp fall on Monday.
Oil prices rose. Brent crude LCOc1 , which fell more than 6 percent on Monday, rose 62 cents a barrel to $57.16, though analysts said the outlook remained weak.
Goldman Sachs said in a note that oil's fall had little to do with Greece and instead reflected oversupply.
Gold XAU= , which has failed to attract much of a safe-haven bid in the latest flare-up over Greece, dipped to $1,165.40 an ounce as the dollar rose.