The jet was downed in conflict-torn eastern Ukraine on July 17, 2014, killing all 298 people on board, including 38 Australian citizens and residents.
Initial findings released last year concluded the Boeing 777 aircraft was shot down by a missile transported from Russia, but Moscow has repeatedly denied any involvement, putting the blame on Kiev.
"My clients have waited three years, Mr Putin. There is still no accountability," Jerome Skinner, an American lawyer representing victims from Australia, Malaysia, New Zealand and the Netherlands, wrote in the Sydney Morning Herald.
"Do you not feel that such tragic loss deserves explanation?... You stand as the only man who can set this right.
"I will use the European Court of Human Rights and every other avenue available to bring the Kremlin to accountability... Meet me and finally make amends for the victims of this tragedy."
Preliminary criminal findings have said around 100 people were under investigation for playing "an active role" in the disaster.
International investigators last month released videos of MH17 relatives talking about the pain of losing their loved ones, in the hope it would spur residents in Ukraine to come forward with new information, Dutch media said.
The European Union last month formally rolled over damaging economic sanctions against Russia, imposed after the shooting down of MH17, for another six months, saying Moscow had failed to live up to its Ukraine ceasefire commitments.
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