The risk of an oil spill, and its impact on such an environmentally sensitive area, was simply too great to consider, Total head Christophe de Margerie said.
"Oil on Greenland would be a disaster," he told Britain's Financial Times in an interview. "A leak would do too much damage to the image of the company."
Royal Dutch Shell, which has spent $4.5 billion and seven years preparing to drill off the Alaskan coast, had to postpone the attempt until next year after a piece of safety equipment was damaged during testing, the newspaper reported.
ExxonMobil, ENI of Italy and Norway's Statoil have signed deals to drill for oil in Russia's Arctic waters and other energy companies have obtained licenses to drill off Greenland.
Total SA has a number of natural gas ventures in the Arctic region, Margerie acknowledged -- saying he was not opposed to Arctic exploration in principle, but noting gas leaks are easier to deal with than oil spills.
Environmental groups applauded his comments.
"The rest of the oil industry should heed his warning," Ben Ayliffe, head of Greenpeace's Arctic campaign, said. "Given the risks, companies shouldn't be touching the Arctic with a barge pole."
The U.S. Geological Survey said in 2008 the Arctic contains more than 20 percent of undiscovered, recoverable oil and gas resources, made more accessible by polar ice cap melting. However, environmental and other factors complicate the exploration and extraction processes.