UPDATE 7-Oil falls to below $65 on recovery doubts

* Oil falls as low as $63.40, lowest since May 28

* Societe Generale says oil expected to average $60 in July

* Nigerian militants say attacked Chevron, Shell oil sites

* US service sector shrinks less in June -ISM survey

(Updates prices)

LONDON, July 6 (Reuters) - Oil fell to below $65 a barrel on Monday and touched a five-week low earlier in the session, pressured by doubts over the prospects for a recovery in the global economy and energy demand.

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. Oil fell even after militants attacked oil installations in major African exporter Nigeria. [ID:nL627910]

"There's a general retreat caused by lack of risk appetite," said Mike Wittner, oil analyst at Societe Generale. "For a couple of months, we perhaps got a bit too optimistic and several markets got ahead of themselves."

U.S. crude CLc1 fell $2.24 from Thursday's close to $64.49 a barrel by 1412 GMT. It traded as low as $63.40, the lowest intraday price since May 28. Brent crude LCOc1 fell $1.30 from Friday's close to $64.31.