Oil prices fell further on Wednesday in line with shares amid tensions over the eurozone's political and economic problems, although bargain-hunting provided support, analysts said.

Crude futures also faced downside pressure following indications by the world's key oil producers that 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, dropped 51 cents to $96.50 a barrel, two days after hitting a near-five month low at $95.34.

Brent North Sea crude for June shed 63 cents to $112.10 a barrel in London midday deals, one day after striking a four-month low at $110.53.

"Oil prices are holding relatively steady as we are seeing a fair bit of investor bargain-hunting in the crude market," said Victor Shum, an analyst at Purvin and Gertz international energy consultants.

"But there remains considerable uncertainty about the eurozone's debt problems and politics," added the Singapore-based expert.

Investor concerns about the repercussions of weekend elections in Greece were heightened 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 forms a new government.

The events in Greece and France -- where Socialist Francois Hollande won Sunday's presidential election -- have stoked anxiety about the eurozone's tough fiscal pact adopted in March to deal with a crippling debt crisis.

Investors were also watching the working relationship between the newly elected Hollande andChancellor Angela Merkel, the leader of Europe's economic powerhouse Germany.

Merkel and outgoing French leader Nicolas Sarkozy played crucial roles in dealing with the eurozone crisis.

"While Mr Hollande's victory in the French presidential elections was in line with expectations, his relationship with Germany's chancellor remains untested," Barclays Bank said in a report.

Crude was also under pressure from indications that Saudi Arabia, the world's top oil producer, could increase its output as it fears that if they remain unsustainably high demand -- and prices -- will fall.