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Activists from 12 countries scaled and occupied Statoil's Transocean Spitsbergen, bound for the Hoop area in the northernmost section of the Barents Sea, and Gazprom's GSP Saturn, on its way to the Pechora Sea.
The activists still remain on the Spitsbergen, suspended by ropes beneath the rig and above the open sea, with Statoil stating its biggest concern is for their safety.
"Statoil respects the right for legal protests and believes it is important with a democratic debate on the oil and gas industry," the company said.
"Statoil has had a dialogue with Greenpeace over the last few months. We have informed about our exploration plans in the Barents Sea and the emergency response setup for the operations on several occasions, and Greenpeace has been given the opportunity to explain their views and ask questions.
"For Statoil, the safety of people and the environment is the first priority, and we do not want activity that can increase the risk level.
"Greenpeace has been explained the risk associated with actions against a rig in open waters. When they still use this form of protest we believe they act irresponsibly and illegally.
"We are concerned for the safety of the demonstrators who have made their way on board, and for the crew."
By contrast, Gazprom took a much harder, and by now, expected course of action, removing the 30 activists occupying the rig after five hours and arresting six of them.
One of the activists on the Statoil rig, a Finnish national named Sini Saarela, was one of the original Artic 30 group imprisoned in Russia in September for protesting Gazprom's Prirazlomnaya oil rig in the Pechora Sea.
Greenpeace has since launched a case against the Russian Federation in the European Court of Human Rights on behalf of its Arctic 30 activists, claiming that they were detained unlawfully.
"I took action in Russia last year to stop exactly the same recklessness as I can see here in Norway," Saarela said.
"We ask everyone to tell the Norwegian government to stop this dangerous rush into the beautiful Arctic environment and rethink its increasingly desperate hunt for oil."
Statoil is unable to drill into any oil-bearing layers in the Hoop area until the complaint from Greenpeace has been dealt with by the Norwegian Ministry of Climate and Environment, which approved the drilling operations on Monday.