The Pchyolki -- a group best-known for advising its members to use violence if necessary to protect churches from "blasphemers" like the rock group Pussy Riot -- filed the suit in January, RIA Novosti reported Saturday.
The suit only became public this week after the group missed a filing deadline for correcting the paperwork.
In court papers, the Pchyolki said the U.S. purchase of Alaska was not legal because the contract specified payment in gold coins and the United States wrote a check for $7.2 million, which would be a far larger sum in today's dollars.
The Pchyolki or Bees, organized in 2008, have a stated goal of protecting orphans' rights. They campaign against sex education in schools and advised, after the Pussy Riot arrests, that the faithful could protect churches by damaging equipment used by "blasphemers" with holy water, although they said "bloodshed" was only acceptable away from church property.
In the lawsuit, the group said Obama's turnabout on same-sex marriage violates the freedom of religion of Orthodox Christians in Alaska, estimated to number about 50,000. The Orthodox "would never accept sin for normal behavior," the group said.