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* Oil falls for the third straight session, heads towards $66

* Rising US, euro zone job losses hit recovery hope (Releads, updates prices)

By Fayen Wong

PERTH, July 3 (Reuters) - Oil steadied below $67 a barrel on Friday, after a nearly 4 percent fall overnight as high jobless numbers across the U.S. and Europe revived concerns about the global economic outlook and its impact on energy demand.

In the latest signal the economy of the world's biggest energy consumer was still struggling with a deep recession, U.S. employers cut a more-than-expected 467,000 jobs in June and the jobless rate rose to a 26-year high of 9.5 percent. [nN02549309]

Euro zone unemployment also rose to 9.5 percent, a 10-year high. [nL2714438]

U.S. crude for August delivery CLc1 edged up 1 cent to $66.74 a barrel by 0607 GMT.

London Brent crude LCOc1 fell 7 cents to $66.58.

"Data from last night were pretty traumatic. We now see the official U.S. unemployment rate at 9.5 percent, which means the real jobless rate could be much higher at 15-16 percent," said Stefano Vincelli, an equities and derivatives broker at Halifax Investment Services in Sydney.

"Also, now that sentiments are getting more bearish, we're again seeing a negative correlation between the U.S dollar and commodities prices."

Analysts said Friday's euro zone service sector surveys for June and retails sales for May are unlikely to cheer investors either, with both sets of data expected to show a deterioration from the previous month.

The dollar held onto gains made in the wake of the U.S. jobs numbers, hovering near its highest in a week against the euro, while Asian stocks retreated on Friday as the bleak jobs data prompted investors to pull back from commodities, resource-linked shares and higher yielding currencies. [ID:nSP536035]

Oil prices have doubled from a low of $32.40 a barrel in December last year and surged over 42 percent in the last quarter -- the largest quarterly gain since 1990 -- amid a weak dollar and optimism that the global economy would rebound by as early as later this year.

But latest economic data worldwide are suggesting that a global recovery will be choppy this year, if it occurs at all. Economists have warned that surging unemployment would be one of the key threats to a sustainable recovery.

JP Morgan said in a report on Friday that it expects oil prices to correct from the recent rally to about $60 a barrel or lower, amid ongoing demand weakness.

"An economic recovery will still be the primary factor in determining oil demand growth. But we are also acutely aware that prices have been rising to ration away the prospect of supply tightness at the end of the year," JP Morgan oil analyst Lawrence Eagles said in the research note.

NYMEX floor trading will be closed Friday for the U.S. Independence Day holiday. Electronic trading will not be affected. (Reporting by Fayen Wong; Editing by Michael Urquhart)