* Oil hits five-week low as equities fall, dollar rises
* Societe Generale says oil expected to average $60 in July
* Nigerian militants say attacked Chevron, Shell oil sites
(Updates prices, adds quote paras 3-4)
By Alex Lawler
LONDON, July 6 (Reuters) - Oil fell to a five-week low towards $64 a barrel on Monday, pressured by doubts over the prospects of an early global economic recovery and a firmer dollar.
The U.S. jobless rate reached a 26-year high and Euro zone unemployment is at the highest in a decade, reports showed last week. The dollar rose on Monday, limiting oil's appeal as an alternative investment, while equities fell.
"It's a definite break to the downside, probably sparked by the poor economic data and stalling stock markets," said Christopher Bellew, a broker at Bache Commodities in London.
"It's completely broken through its support at around $68.00-$68.50 and technically and probably fundamentally, heading lower now," he added, referring to Brent crude.
U.S. crude <CLc1> fell $2.47 from Thursday's close to $64.26 a barrel by 0934 GMT. It traded as low as $63.85, the lowest intraday price since May 28. Brent crude <LCOc1> fell $1.51 from Friday's close to $64.10.
NYMEX floor trading was closed on Friday because of the U.S. Independence Day holiday, and although oil traded electronically the exchange did not issue an official closing price.
Adding to pressure on oil, European stocks <.EU> got off to a weaker start on Monday following on from losses in Asia. U.S. stock futures pointed to a lower opening on Wall Street.
Investors will focus later this week on a meeting of the G8 industrial nations. The summit was expected to highlight signs that economies were stabilising, but emphasise that it was too early yet to withdraw policy stimulus.
Societe Generale said the correction in oil prices, which surged 42 percent in the last quarter, was long anticipated and predicted that oil prices would continue falling and average around $60 a barrel in July.
"Non-fundamental price support, based on economic optimism, risk appetite, and increasing medium to long-term inflation expectations, has faded for now," Michael Wittner of SG said in a research note.
Attacks on oil installations in Nigeria, traditionally Africa's top oil producer, could limit losses.
Chevron, Shell and Italian energy firm Agip <ENI.MI> have cut oil output by around 273,000 barrels per day in the last six weeks following the latest campaign of militant violence. (Additonal reporting by Fayen Wong in Perth; Editing by William Hardy)