Oil prices are sharply down from the record reached in July
The price of Brent crude has risen from its earlier 20-month low after reports suggested Saudi Arabia had already cut production to support world prices.
Brent crude rose $5.43 to $65.91 a barrel after falling as low as $58.38 during the session in London.
US light, sweet crude traded at $69.88 having peaked at $71.77.
Reports said Saudi Arabia had reduced its exports of oil by 900,000 barrels a day from their peak in August, with other oil producers following suit.
Saudi Arabia is the biggest oil exporter in the world.
Tim Evans at City Futures Perspective says the market is driven now by "a trio of supportive factors; a weaker US dollar, a push to the upside in global equity markets and market talk that Saudi Arabia may have already cut crude oil production."
Members of the Opec oil producers' cartel agreed in October to cut crude supplies by 1.5m barrels a day to boost prices, but investors had been waiting to see when the cuts would be implemented.
Earlier on Tuesday Brent crude fell to its lowest level since February 2007 amid concerns about the state of the US economy.
Oil prices have slumped since hitting a record of $147 a barrel in July, as consumers have cut their spending and the chances of a global recession have grown.
Credit Suisse has also cut its forecast for China's energy demand, predicting that it will remain unchanged in 2009.
Recent figures showed China's economic growth rate fell for the third quarter in a row, prompting fears of a wider downturn.
Growth slowed to an annual pace of 9% in the three months to September - down from 10.1% over the previous quarter.
There had been hopes that growth in developing nations such as China and India would help offset the slump in demand in US.