Crude futures also faced downside pressure following indications by the world's key oil producers they may boost output to bring prices down to sustainable levels.
New York's main contract, West Texas Intermediate (WTI) crude for delivery in June, was down 39 cents at USD 96.62 per barrel while Brent North Sea crude for June shed 58 cents to USD 112.15 in morning trade.
"Oil prices are holding relatively steady as we are seeing a fair bit of investor bargain-hunting in the crude market," said Victor Shum, senior principal at Purvin and Gertz international energy consultants in Singapore.
"But there remains considerable uncertainty about the eurozone's debt problems and politics," he added.
Investor concerns about the repercussions of weekend elections in Greece were heightened on Tuesday after the head of the country's left-wing Syriza party said his cabinet would reject all austerity measures imposed under an EU-IMF loan deal, if he managed to form a new government.
The political developments in Greece as well as in France where Socialist Francois Hollande emerged victorious on Sunday's presidential election have stoked anxiety about the fate of the eurozone's tough fiscal pact adopted in March to deal with a crippling debt crisis.
Crude prices were also under pressure by indications that Saudi Arabia, the world's top oil producer, could increase its output to scale down prices.
Saudia Arabia and other key oil-exporting nations fear that unsustainably high prices will have a drastic impact on demand, pushing prices lower.