Oil rose by more than $1 on Tuesday after slumping 10 percent slump 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 $1.26 at $41.41 a barrel by 8:48 a.m. EST, after tumbling $4.61 overnight, while London Brent crude rose $1.34 to $43.55 a barrel.

European shares fell on Tuesday, with a key index hitting a lifetime low as investors sold out of the banking sector and concerns about the health of the global economy weighed on sentiment. <.EU>

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, but analysts expect more cuts by the producer group 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.

World equities plumbed multi-year lows on Monday and the dollar climbed to nearly three-year highs as a record quarterly loss for U.S. insurer AIG fueled fears over the financial sector and boosted the greenback's safe-haven status.

The Dow Jones stock index <.DJI> fell below 7,000 for the first time since October 1997 after American International Group reported the biggest quarterly loss in U.S. corporate history at $61.7 billion.

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 by Jennifer Tan in Singapore; editing by James Jukwey)