|Cairn Offshore Drilling|
Eleven activists in rock-climbing gear used speedboats to intercept and then climb on to the Leiv Eiriksson after it had left a port in Istanbul.
They climbed the rig's derrick, unfurling a banner that read: "Stop Arctic destruction" and "Go Beyond Oil, Choose Clean Energy".
The platform, bound for Greenland's Baffin Bay, did not stop and was continuing on its course, heading towards the Dardanelles strait with the activists on board, Deniz Sozudogru, a Greenpeace spokeswoman for the Mediterranean region, said.
There were no Turkish coastguard boats trailing the oil rig, she said. The Dardanelles connects the Sea of Marmara to the Aegean sea.
Activists from Britain, Denmark, Canada, Poland, Germany, Slovakia, Austria, Sweden and Turkey were prepared to occupy the rig for days, according to the group.
It said the oil rig, operated by Scottish company Cairn Energy, has "a very short window in which to drill their four new exploratory wells" due to extreme weather conditions in the Arctic.
Cairn Energy confirmed an "incident" involving Greenpeace off Turkey's coast and said the vessel was continuing "in transit to take part in Cairn's 2011 exploration programme in Greenland."
The company said it was operating at the invitation of Greenland's government and had successfully drilled three wells there in 2010.
Officials added: "Wherever it is active, Cairn seeks to operate in a safe and prudent manner. Cairn respects the rights of individuals and organisations to express their views in a safe manner."
Greenpeace wants Cairn to suspend deep-water drilling after the spill in the Gulf of Mexico.
"Freezing temperatures, severe weather and a highly-remote location pose unprecedented challenges to any oil in the Arctic and mean a spill could be impossible to contain and clean up," Greenpeace said.
Leiv Eiriksson, one of the world's largest rigs, had been exploring possible oil and gas in the Black Sea under a joint venture between Turkey and Brazil's Petrobas.