The organization said more than 40 environmental groups signed a letter to President Vladimir Putin requesting the release of the Arctic Sunrise and the 30 people reported aboard, RIA Novosti reported.
Russian border guards said the ship was involved in "piracy" when they seized it Thursday in the Pechora Sea in international waters inside Russia's exclusive economic zone, officials said.
Greenpeace activists had scaled the rig the day before, the officials said.
The letter, written by Russian branches of domestic and international environmental groups, said the activists had "acted peacefully" in attempting to bring public attention to oil production projects they considered "environmentally unacceptable."
The Arctic Sunrise entered waters off the Russian coast last month despite a Russian sailing ban Greenpeace called unlawful.
The ship is expected to arrive Tuesday in the Russian port of Murmansk.
If convicted of piracy, crew members of the Arctic Sunrise face up to 15 years in prison, officials said.