The Investigative Committee said in a statement that the charge, which can result in a 15-year prison term upon conviction, was filed Thursday against 16 members of the crew, including a prominent Russian freelance photographer.
The crew's other 14 members were similarly charged the day before.
In addition to Russia the activists hail from 17 other countries: Argentina, Australia, Brazil, Canada, the Czech Republic, Denmark, Britain, Finland, France, Italy, the Netherlands, New Zealand, Poland, Sweden, Turkey, Ukraine and the United States.
The Russian Coast Guard seized the Greenpeace ship and all the people it was carrying following the Sept. 18 protest at the offshore platform owned by Russian state-controlled energy giant Gazprom. The activists are now in custody in the northern city of Murmansk.
Greenpeace denies any wrongdoing and describes the charges as absurd.
The platform, which belongs to Gazprom's oil subsidiary, is the first offshore rig in the Arctic. It was deployed to the vast Prirazlomnoye oil field in the Pechora Sea in 2011, but its launch has been delayed by technological challenges. Gazprom said in September that it was going to start pumping oil this year but did not provide the exact date.