By early afternoon in Europe, benchmark West Texas Intermediate crude for July delivery was down 24 cents to US$82.46 per barrel in electronic trading on the New York Mercantile Exchange.
Earlier on Tuesday, oil dropped to US$81.07, the lowest since October, after having dropped $1.40 a barrel on Monday.
In London, Brent crude for July delivery was down 72 cents at US$97.37 a barrel on the ICE Futures exchange.
Crude jumped temporarily on Monday after the 17 countries that use the euro common currency pledged to lend Spain US$125 billion to rescue its faltering banks. However, attention soon turned to the Greek election this weekend, the outcome of which could determine if Greece stays in the euro.
"There are highly uncertain and fragile economic conditions across the eurozone that dominate the markets and cause nervous trading and volatility," said analysts at Sucden Financial in London.
Oil has plunged about 24 per cent from US$106 a barrel since early last month amid signs of slowing economic growth in the U.S., China and Europe.
Traders will also closely watch a quarterly meeting of the Organization of Petroleum Exporting Countries in Vienna on Thursday. Some members of the cartel have suggested recently that OPEC is producing too much crude and the group could decide to cut supplies to help boost prices.
An OPEC report showing oil output at its highest in the last four years is sure to be used by price hawks such as Iran and Venezuela. The monthly report, published Tuesday, showed OPEC production just short of 33 million barrels a day. That's almost three million barrels more than the organization's overall quota and more than 630,000 barrels above the May figure.
The report said it expected world demand this year to increase by 900,000 barrels a day while saying at the same time that economic uncertainty might upend that prediction and lead to "a further decline in world oil demand."
Saudi Oil Minister Ali al-Naimi said, however, that OPEC needed to raise its production target of 30 million barrels a day.
Al-Naimi's remarks indicate "that the world's leading oil supplier has no intention of cutting back on production despite recently lower prices and an apparent oversupply in the market," said a report from JBC Energy in Vienna.
"If production remains at its current level, the global oil market risks seeing a supply surplus of well in excess of one million barrels per day in the second half of the year, which would exert further pressure on oil prices," said analysts at Commerzbank in Frankfurt.
In other energy trading, heating oil was unchanged at US$2.6357 a U.S. gallon (3.79 litres) while gasoline futures fell 1.13 cents to US$2.6453 a gallon. Natural gas lost 1.4 cents to $2.204 per 1,000 cubic feet.
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