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New York's main contract, light sweet crude for delivery in April, added 19 cents to $91.01 a barrel and Brent North Sea crude for April delivery rose 53 cents to $112.14.
"Oil is trading... higher with a touch of uncertainty in the (Latin American) region," said Jason Hughes, head of premium client management at IG Markets Singapore.
He said the impact of left-wing leader Chavez's death has yet to be fully felt but traders are watching for signs of instability in Venezuela, a member of the Organization of the Petroleum Exporting Countries.
"It will be interesting to see how things develop," given that Venezuela is a major OPEC producer and "there is a potential for instability in the country," he told AFP.
Chavez, 58, lost his battle with cancer on Tuesday, plunging the oil-rich nation into an uncertain future.