Brent crude futures were trading at $48.84 per barrel at 0422 GMT, up 26 cents from their last settlement, while U.S. crude was up 35 cents at $48.20 a barrel, according to Reuters.
Both oil benchmarks had climbed on Tuesday after markets shook off some of shock from the referendum in Britain in which most voters elected to exit the EU.
"Oil led the (commodities) sector as the shock of the UK voting to leave the EU wore off. Oil gains were solidified by news that the decline in Venezuela's oil output appears to be accelerating, while a strike in Norway also looked like it would impact production," ANZ Bank said.
A looming strike by Norwegian oil workers threatened to cut output from the biggest North Sea producer, according to the report.
In crisis-struck Venezuela, oil producers and refiners were struggling to keep output up due to power outages and equipment shortages also supported prices, traders said, according to Reuters.
Additionally, the American Petroleum Institute indicated in a report on Tuesday that U.S. crude inventories fell nearly 4 million barrels for the week to June 24, some two-thirds more than the 2.4 million barrels expected by analysts.
The U.S. Energy Information Administration will issue official stockpile data on Wednesday.
