New York's main contract, light sweet crude for delivery in May, added 31 cents to $106.56 a barrel.
Brent North Sea crude for May delivery gained 48 cents to $121.40 a barrel in London deals.
"Prices rebounded from two days of heavy losses and corrected higher, following stronger equity markets in Asia and eurozone, while the US dollar remained fairly weak, adding further support," said Sucden analyst Myrto Sokou.
"The geopolitical situation in Libya and Middle East continue to remain fairly uncertain, giving mixed signals.
"Therefore, it (the oil market) is likely to experience some consolidation in the short-term, as crude oil prices are struggling for some direction."
At 1430 GMT, the US government's Energy Information Administration (EIA) will publish its weekly inventories report.
American crude reserves are predicted to rise by 1.1 million barrels in the week to April 8, according to analysts polled by Dow Jones Newswires.
Gasoline or petrol stocks are expected to drop 0.7 million barrels, while distillates -- which include diesel and heating fuel -- are forecast to slide by 3.7 million barrels.
Oil prices had fallen Tuesday after US bank Goldman Sachs warned that commodity markets were showing signs that the high prices were eroding demand.
"Crude oil prices plunged heavily on Tuesday after a bearish report from Goldman Sachs weighed heavily in most commodity markets and prompted investors to profit-taking, driving to a heavy sell-off in crude oil and base metals prices," added Sokou.
Also on Tuesday, the International Energy Agency (IEA) and the Organization of Petroleum Exporting Countries (OPEC) published bearish oil demand forecasts.
The Paris-based IEA issued a grim warning that recent high price levels have hurt global energy demand.
It said that "there are real risks that a sustained $100-a- barrel-plus price environment will prove incompatible with the currently expected pace of economic recovery."
The agency said in its monthly report that "global oil demand growth has shown signs of slowing in recent months in the face of sharply higher prices."
The International Monetary Fund had already warned on Monday that high oil prices were a key risk to global economic recovery.
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