The deal will allow a consortium of energy companies Total and ExxonMobil with Greece's Hellenic Petroleum to explore two areas that are together about the size of Switzerland - 40,000 square kilometers (15,000 sq. miles) - south and southwest of the island of Crete.
It's the latest and by far biggest in a series of concessions for oil and gas exploration in the west of the country.
Fears of confrontation with neighboring Turkey over energy extraction rights have precluded similar deals in the Aegean Sea and east of Crete. Turkey currently has a drilling ship, escorted by warships, in waters where Cyprus has exclusive economic rights, and has threatened to make similar moves further west.
Greenpeace and the World Wide Fund for Nature have appealed to Greece's supreme court to block the Crete project. They say prospecting in deep waters off the southern island will threaten endangered whales, dolphins and other marine life, and argue that Greece would do better to invest in renewable energy to help fight global warming.
Left-wing Prime Minister Alexis Tsipras hailed Thursday's signing as a boon to the economy and promised "the strictest" environmental safeguards.
"Greece is making a determined move to exploit its mineral wealth," Tsipras said at the ceremony in Athens, saying the deal would help an economy battered by a decade-long financial crisis that resulted in three international bailouts - the last signed in 2015.
"Four years ago this was a country on the brink of bankruptcy," Tsipras said. "Now it aims to attain energy self-sufficiency, or at least to cover part of its requirements."
He said the exploration would start next year, last eight years with an option for extension, and should provide "a clear picture" of potential deposits in 2-4 years. Greece stands to receive just 8 million euros from the concessions, but also revenues and taxes from any profits.
WWF Greece marine officer Dimitris Ibrahim told The Associated Press that the signing marked a "dark day" for the country.
"For a very small price, a huge area with enormous environmental value is being conceded," he said. "The sea is very deep, therefore any drilling would be very dangerous. ... The slightest accident resulting in pollution in an area so significant for tourism (as Crete) would have vast financial repercussions."
The tract of seabed conceded includes a large section of the Hellenic Trench, a deep undersea depression that describes an arc from the northwestern island of Corfu, past Crete to the Turkish coast. It's a vital habitat for the Mediterranean's few hundred endangered sperm whales - already threatened by fishing nets, ship strikes and plastic pollution - and other species of whales and dolphins.
These mammals are particularly sensitive to the underwater noise produced by seismic surveys for fossil fuels, in which sound waves are bounced off the seabed. Sonar used by warships has been shown to have deadly effects on whales, and experts say seismic surveys can do the same.
Last month, dozens of leading environmental groups and scientists wrote to Tsipras warning against the concessions, but Ibrahim said they received no answer.
He said WWF will exhaust all legal means to fight the project.
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