The organization said the six climbers were in places they could not be reached and had supplies for several days.
Workers on the Prirazlomnaya rig in the Pechora Sea used water cannons in an effort to keep the activists off, ITAR-Tass reported. Kurt Naidoo, the environmental group's chief, was one of those on the rig.
In an "Open Letter to the People of Russia" posted on the Greenpeace Web site, Naidoo said that oil drilling on the continental shelf in the arctic could cause environmental havoc. He said Russia could get the same amount of fuel by stopping leaks in existing systems.
Gazprom, the state oil company, appears ready to start drilling in the arctic without viable plans to respond to spills, Naidoo said.
The raid was launched from a Greenpeace ship, the Arctic Sunrise.
"This is the face of arctic destruction. Prirazlomnaya is the first ice-capable permanent oil platform in the Arctic. It is a perfect example -- it is a personification of the slowly creeping industrialization of this pristine area," Dima Litvinov, a Greenpeace spokeswoman, said from the ship. "And especially, given the information that is coming in all the time about the rapidly decreasing ice cover in the arctic, it is an obscenity. It is an insult that the same companies that are responsible for this crisis are now seeking to profit from it."