Russia on Tuesday opened a piracy probe over a Greenpeace protest against the Arctic oil activities of the Gazprom energy giant, saying it will prosecute all activists involved.

Investigative Committee spokesman Vladimir Markin said a criminal probe for piracy undertaken by an organised group had been opened over Greenpeace's September 18 protest on a Gazprom oil rig in the Barents Sea.

"It should be noted that all persons who attacked the (oil) platform, regardless of their citizenship, will be brought to criminal responsibility," Markin said in a statement.

The Dutch-flagged Arctic Sunrise had been monitoring the exploration activities of Gazprom since August in the hope of exposing the dangers of drilling for oil in one of the world's great nature reserves.

Russian security forces seized the global environmental lobby group's ship and its 30-member crew a day after two activists from Finland and Switzerland climbed up the side of a Gazprom platform to draw attention to its controversial work.

The two were detained after Russian navy patrol boats opened warning shots at the ship. They and the entire crew were later placed under arrest and locked up in the Arctic Sunrise's mess.

The group says the Russian action was illegal because the Arctic Sunrise was in international waters at the time of the raid.

But Markin argued that the Greenpeace ship was located "in the exclusive economic zone of the Russian Federation" when it was boarded by agents from Russia's Federal Security Service (the main successor to the Soviet-era KGB).

It was not immediately clear from Markin's comments whether the investigation had been launched against just the two activists who had attempted to scale the platform or all activists on board the ship.

The Arctic Sunrise was approaching the shoreline of Russia's Far Northern city of Murmansk on Tuesday after being tugged from the scene of the action by a Russian border guards boat.