By Rebekah Kebede
The news offset a report by the U.S. Energy Information Administration further revising down its forecast for 2009 global oil demand.
U.S. crude settled at $37.78 a barrel, up 19 cents, off a session high of $39.50. February Brent settled at $44.83, up $1.92.
"This is a product-led rally, with heating rallying on cold weather and gasoline up with the crack spread up dramatically. News that the Saudis have cut production a lot is also supportive," said Andrew Lebow, broker at MF Global.
Saudi Arabian Oil Minister Ali al-Naimi said the world's biggest exporter would pump below its OPEC production target of 8.05 million bpd in February.
"If there is a need to do more, we will do so because our purpose is to bring things in balance," Naimi told reporters in New Delhi. "We will look and see whether we need to take more. If we need to, if inventories keep rising, we will reduce."
"We have taken -- Saudi Arabia alone -- 1.7 million (bpd)" (off the market), he said.
OPEC's secretary general said the cartel may cut oil output further at its meeting in March if the market remains oversupplied a month from now.
OPEC agreed to cut supply by 2 million bpd at meetings in September and October. In December, it agreed to lower output by a further 2.2 million bpd as of January 1, a record reduction.
Support also came from a blast of cold winter weather in the northern hemisphere, which pushed up heating oil futures.
The global economic crisis has dented global energy demand and helped send crude prices tumbling from record highs over $147 a barrel hit in July.
Earlier in the day, oil prices turned negative as demand concerns overshadowed the U.S. cold front and Saudi Arabia's cuts.
The EIA revised down its 2009 world oil demand forecast by 200,000 barrels per day (bpd) on Tuesday, calling for consumption to fall by a total of 810,000 bpd this year compared with 2008 levels.
"The demand was revised downward, but (the) decline in global demand for 2009 looks rather small when measured against a 4.2 million barrels per day drop in OPEC quotas," said Tim Evans.
U.S. crude oil stocks have swelled as demand in the top oil consumer wilts, pushing U.S. crude futures into a deep discount compared with Brent crude.
Stock levels at Cushing, Oklahoma, the delivery point for U.S. crude futures, have hit record levels and analysts expect inventories could rise further.
A Reuters poll ahead of Wednesday's U.S. inventory report forecast crude stocks rose by 2.2 million barrels last week, the third weekly gain.
Russia started pumping gas meant for Europe via Ukraine on Tuesday for the first time in nearly a week, but the European Union said little or no gas was flowing to countries suffering urgent energy shortages.
(Additional reporting by Gene Ramos and Robert Gibbons in New York; Christopher Johnson and David Sheppard in London, Fayen Wong in Perth and Chua Baizhen in Singapore; editing by Jim Marshall)