Last week lawyers for the Arctic 30 asked the committee to contact the Federal Migration Service (FMS) and request visas for the non-Russians, so they could leave Russia and return if summoned by the authorities.
But in its letter to Anne Mie, the committee said it was not willing to ask the FMS to issue the visas. The FMS had previously said it would not issue visas until it received a direct request from the committee.
Arctic Sunrise captain Peter Willcox, who was among those arrested, described the situation as farcical.
"We were seized in international waters and brought to Russia against our will, then charged with a crime we didn't commit and kept in jail for two months.
"A respected international court says we should be allowed to go home, so do numerous Presidents and Prime Ministers, but we can't get visas to leave the country, and even if we could there's no guarantee the Investigative Committee won't schedule an interview for the day I get home, forcing me to break my bail conditions.
"This is either a mistake and we're caught in a vicious bureaucratic circle, or it's a deliberate snub against international law. Either way this is a farce.''
A ruling last month by the International Tribunal for the Law of the Sea ordered Russia to allow the group to leave the country and to release the Greenpeace ship Arctic Sunrise, as soon as a bond of 3.6m euros in the form of a bank guarantee was paid, Greenpeace said.
That bond was posted by the Netherlands Government - where the Arctic Sunrise was registered - last month.
Greenpeace International legal counsel Daniel Simons said the Russian Federation was in clear breach of a binding order of an international tribunal.