In New York trading, a barrel of oil could be bought for $US27.95, down US20c while in London, crude was trading at $US26.38 bbl, down US18c.
Last month, Venezuelan output was 2 per cent below quota. This is in stark contrast to when Mr Chavez assumed office in late 1998, when Venezuelan exceeded its output by 4% and the price of oil was about $US10 bbl.
Venezuela has the largest proven oil reserves outside of the Middle East, supplies about one-sixth of US crude oil imports and is OPEC's third largest producer.
Last month, an eight-day strike at Petroleos de Venezuela SA triggered a nationwide walkout and violent street protests that led to the failed military coup on April 11.