Two members of the group were detained Sept. 18 in their attempt to scale the Russian Arctic platform.
The coast guard seized Greenpeace's ship the next day and towed it with the 30 activists aboard, to Murmansk.
The activists from 19 countries are in custody and being investigated for piracy.
The court is expected to rule Thursday whether to dismiss the case and release the activists or keep them in jail pending the probe. Investigators said they are seeking the activists' arrest.
Though Russian President Vladimir Putin said Wednesday that the activists aren't pirates, he defended the detention by saying coast guard officers.
Two Canadians are among those who could find themselves embroiled in the Russian legal system.
Paul Ruzycki of Port Colborne, Ont., was serving as the ship’s chief mate when it was seized last Thursday. A Canadian from Montreal whose name has not been released was also on board.
_ With files from The Canadian Press.