Four Greenpeace activists who had clung to a British-owned oil rig off Greenland with rock-climbing gear have been arrested after an Arctic storm forced them to abandon their environmental protest.

The four men - from the US, Finland, Poland and Germany - faced preliminary charges of violating a 500 metre security perimeter around the Stena Don rig and trespassing by climbing onto the installation.

The activists had been suspended under the rig since Tuesday to protest at Cairn Energy's deepwater drilling in the area, saying it could spark an oil rush in sensitive Arctic waters.

Greenpeace said it contacted police to say the men were giving up because of rough weather.

"We stopped this rig drilling for oil for two days but the campaign is far from over," Greenpeace spokesman Jon Burgwald said by telephone from the ship Esperanza, which is anchored off Greenland.

"Our activists hung there for more than 40 hours but last night, a freezing storm and high waves made them decide it was too risky. So we contacted the police to say we were stopping the action," he said.

Danish police spokesman Morten Nielsen said the four men were being held in Greenland. They could face fines, prison terms or deportation.

"Police were in a situation where they had to save and help some of them up because they had gotten themselves into a difficult situation," he said.

He said police seized a Greenpeace helicopter on Greenland on the grounds that it could be used as evidence in the investigation.

Greenland is a semi-autonomous Danish territory, and police have been monitoring the activists from a Danish navy ship patrolling the area since the activists arrived on August 16.