Oil rose slightly on Tuesday after slumping 10 percent in the previous session, but showed little sign of a strong recovery as falling crude demand overshadowed OPEC's production cuts.

U.S. crude was up 65 cents at $40.80 a barrel by 9:53 a.m. EST, after rising as high as $42.07, while London Brent crude rose 83 cents to $43.04 a barrel.

Traders said the move to the session high came after Royal Dutch Shell Plc said it had shut a number of oil installations at its Nigerian venture following explosions on a pipeline.

But that move was shortlived against the background of wider economic weakness. World stocks took yet more losses on Tuesday, with European shares hitting a record low, a day after most equity markets suffered a thorough battering at the hands of investors fearful for the global financial system.

OPEC oil supply fell in February for a sixth straight month as members enforced a deal to cut output and prop up oil prices, a Reuters survey showed on Monday, and analysts saw more cuts by the producer group as possible when it meets in Vienna on March 15.

OPEC could help prices if it decides to cut production again at its March meeting, said Sucden Financial trader Robert Montefusco.

However, with the recession we're witnessing, OPEC is probably only capable of stopping prices from crashing even lower than really boosting them higher.

United States oil inventory figures on Tuesday and Wednesday will show the impact on demand from the world's top energy consumer and February unemployment and non-farm payroll data on Friday will shed more light on the state of the U.S. economy.

Global oil demand is expected to fall sharply in 2009, following a slight contraction last year. World oil consumption last fell in the early 1980s.

Mixed macro-economic data out of top energy-consumer the United States on Monday showed milder shrinkage in manufacturing and a slight bounce in consumer spending, but the improvement was likely a blip in a rapidly deteriorating economy.

(Additional reporting Robert Gibbons in New York; editing by William Hardy)