Mohammed Al Hamli said oil supplies were "sufficient currently" and there was no need for an emergency meeting.
Consumers have been urging the 12-member group to produce more oil to lower prices.
London Brent crude, currently seen as a better gauge of the global market than US oil, was up 12 cents at $71.14 a barrel. US crude was up 91 cents at $66.87.
"The market is reacting to the Opec president saying the group has no intention of raising output," said Nauman Barakat, senior vice president at Macquarie Futures USA.
Data showing US refiners were struggling to boost summer petrol production and Cyclone Gonu's disruption of Omani oil and gas exports also kept Brent crude within sight of late May's $71.80 high.
Weekly US inventory data showing a surprise drop in refinery utilisation rates last week added to gains, overshadowing an unseasonally large 3.5 million barrel build in petrol stocks thanks to a surge in imports.
With petrol stocks still nearly 10m barrels shy of normal and refiners utilisation falling to below 90pc, the weakest early-June level in 15 years, traders remained anxious over driving season supplies.
US winter heating oil stocks are 16pc below the five-year average, noted Frederic Lasserre, head of commodities research at Societe Generale Corporate and Investment Banking. Already some investors are looking beyond the summer to winter demand in the world's top consumer.
