The compensation claim was filed with the Strasbourg-based court by Sydney legal firm LHD Lawyers on May 9 on behalf of 33 next of kin from Australia, New Zealand and Malaysia, the The Sydney Morning Herald said.
All 298 passengers and crew -- the majority of them Dutch -- died when the Boeing 777 was hit by a Russian-made BUK anti-aircraft missile over war-torn eastern Ukraine on July 17, 2014.
Jerry Skinner, a co-associate of LHD whose signature is on the claim, told the Herald that his clients wanted accountability.
"They want enough money to reflect that the Russians take this seriously," the paper quoted Skinner as saying.
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Officials with the Dutch Safety Board (OVV) concluded last year as part of an international investigation that the Boeing 777 was hit by a BUK missile.
In February, a separate criminal investigation team said they hoped within months to pinpoint the exact spot from which the missile was fired.