On Friday, the contract dropped nearly $3 to settle at $40.81. Prices fell as low as $40.50, levels last seen in December 2004.
In London, January Brent crude rose $1.60 to $41.34 on the ICE Futures exchange.
Chakib Khelil, president of the Organization of Petroleum Exporting Countries, said Saturday the group could announce a "severe" reduction of output quotas at its next meeting on Dec. 17 in Algeria.
The OPEC head would not specify how deep the output cut would be, but noted that some analysts are predicting a decrease of as much as 2 million barrels per day.
An output decision that startles markets would help bolster plunging oil prices, Khelil said in an interview with The Associated Press.
"The best way is to surprise them," he said. "I hope it will."
OPEC will likely cut production by at least 1 million barrels a day, said David Moore, commodity strategist with Commonwealth Bank of Australia in Sydney.
"The possibility of OPEC moving to tighten up the oil market is real," Moore said. "As we get closer to the meeting, people may get more wary that OPEC may make a large cut."
OPEC announced a production cut of 1.5 million barrels a day in October and investors largely ignored it, focusing instead on a global economic slowdown that has weakened crude demand.
KBC Market Services in Great Britain suggested OPEC would need to introduce a pricing mechanism to avoid excessive peaks and valleys and stabilize oil prices, one of the cartel's stated objectives.
"The extremes of price are very damaging. High prices hasten and intensify recession while low prices undermine producer revenues and cut investment in marginal supplies," KBC said in its monthly oil market outlook. "The purpose of oil market management is to avoid such extremes."
The price of oil has fallen about 70 percent since peaking at $147.27 in July.
President-elect Barack Obama warned Sunday that the U.S. economy, which saw the worst jobs data in 34 years on Friday, would get worse before improving.
"Pessimism about the international outlook has remained intense," Moore said. "Concerns about weakening oil demand have not gone away. You have to look at today's movement in the oil price in light of the ferocious decline over the past week."
On the other hand, U.S. President-elect Barack Obama's plans for the largest U.S. public works spending program in 50 years and his aim to create 2.5 million jobs over his first two years in office helped boost oil prices
"The market is also hoping there would be an increase in demand for raw materials as a result" of Obama's intended policies, London's Sucden Research said in a report.
In other Nymex trading, gasoline futures rose 4.59 cents to 94.71 cents. Heating oil gained 6.26 cents to $1.4891 a gallon while natural gas for January delivery slid 17 cents to 5.572 per 1,000 cubic feet.
Associated Press writer Alex Kennedy in Singapore contributed to this report.
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