Brent North Sea crude for delivery in April jumped $2.33 to $110.85 a barrel in late London trading. The contract had slumped by $5.15 on Tuesday.
New York's main contract, light sweet crude for April rose 89 cents to $98.06 a barrel on Wednesday, after plunging $4.01 the previous day.
The market has been on tenterhooks over the nuclear crisis this week because Japan is the world's third biggest economy, and is also the third largest global consumer of crude oil.
"Undoubtedly, the short term is likely to see some adverse demand impact, with the main sources of genuine demand reduction being the shutdown of damaged thermal power plants, the loss of some petrochemical capacity, and the general reduction in activity caused by dislocations and damage to economic infrastructure," Barclays Capital analysts said Wednesday.
"The oil market's reaction to the Japanese earthquake is overdone, in our view, given the potential increases in oil demand resulting from the permanent loss in nuclear capacity far outstripping the short term negative impact on demand," they added in a note to clients.
Japan's nuclear crisis deepened Wednesday with another fire at a quake-hit atomic power plant and a radiation spike there that forced the temporary evacuation of workers.
The oil market meanwhile found support from fresh unrest in the Middle East, where Bahrain has declared a state of emergency in a bid to quell protests.
Popular uprisings in the Middle East and North Africa, which toppled the leaders of Tunisia and Egypt, had been driving oil prices higher on concerns over supply disruptions.
Libyan strongman Moamer Qadhafi, who is facing a bloody, month-old uprising, has vowed to crush the rebellion.
Elsewhere, the US Department of Energy announced Wednesday that its crude stockpiles rose by 1.7 million barrels last week, while inventories of gasoline, or petrol, slumped by 4.2 million barrels.
Analysts had forecast a smaller rise in crude of 1.1 million barrels and a drop of only 1.8 million barrels for gasoline in the United States, the world's biggest oil-consuming nation.