The company split its shares between the autonomous provincial government and the national government in Port Moresby.
But Bougainville is furious that it was not given all the shares, and that Rio Tinto said it is was no longer obliged to do anything about the damage caused by the Panguna mine, which sparked a civil war that lasted through the 1990s.
The province hoped to reopen the mine as a way to generate revenue should it vote to become independent from PNG after a referendum scheduled for 2019.
Last month, the autonomous government held an emergency session of its parliament and issued a number of resolutions.
"My government, and all Bougainvilleans, oppose the shares in BCL being transferred to the PNG government. The justification for the transfer advanced by Rio has no basis," John Momis, Bougainville's president, told parliament.
"Equal PNG shareholding with the ABG raises the same grave dangers for the future of peace in Bougainville," he said.
"Moreover, its decision on allocating shares was clearly made in close consultation with PNG, and without consulting the ABG. Perhaps they both forgot that the mineral resources BCL was established to mine are located in Bougainville. Perhaps they forgot that Bougainville is autonomous, and has full power over mining. "
Bougainville accepted its 36.4 percent of BCL but will negotiate with the PNG Government for it to surrender the Rio Tinto shares it was given.
"There is a deep history of conflict and bitterness in Bougainville over the impacts of the Panguna mine. Since 2014 I have been advising the Prime Minister, in the strongest terms, that it is impossible for Bougainvilleans to accept National Government control of Panguna through control of BCL," said Mr Momis.
The ABG called for Bougainville-wide unity as it launched what it said would be the strongest possible international campaign to pressure Rio Tinto to accept its responsibility for the mine's legacy issues and that it would pursue the company in the courts.
"It is grossly unjust - completely unacceptable - for Rio to now refuse any responsibility for the long-term impacts of the operations of its subsidiary, BCL. They told me they can walk away because they operated the mine under the PNG legal standards of the 1960s, 1970s and 1980s. But it was clear in the 1980s, at least, that the standards of the day were appalling. It was the injustice of those terrible standards that caused the conflict," said Mr Momis.
Bougainville also intends taking up the legacy issues with both the PNG and Australian Governments.