The Parti Quebecois is also considering legal steps to force Ottawa to reveal what Pierre Elliott Trudeau's Liberal government did at the time.
Intergovernmental Affairs Minister Alexandre Cloutier called on Supreme Court Chief Justice Beverley McLachlin on Wednesday to announce her intentions, saying she "must respond to questions" that have arisen.
Cloutier told a news conference in Quebec City that McLachlin must convene an independent inquiry with a precise mandate.
"We want to know if the inquiry is going to be independent, how much it will cost and how long it will last," Cloutier said before a PQ caucus meeting.
"We want to know the mandate that will be given to commissioners, to investigators (and) we want to know precisely what it's all about."
A spokesman for the high court says the allegations contained in a new book by historian Frederic Bastien are being looked into.
Bastien writes that Bora Laskin, then chief justice of the Supreme Court, provided information to the Canadian and British governments on the discussions between magistrates about the legality of repatriation.
Another high court judge, Willard Estey, also secretly advised the British government in 1980 that the Supreme Court would address the issue, the author writes.
Bastien suggests both jurists violated the principle of separation of executive and judicial powers. He gathered information during eight years of digging through documents, including British Foreign Office archives.
Cloutier said Prime Minister Stephen Harper's government has no choice but to tell Quebecers exactly what happened, pointing out Ottawa can't ignore "a concrete case of intervention" of the court into the country's political affairs.
"Canada cannot do nothing," Cloutier said. "This is extremely serious. This is a concrete case of (political) intervention by the highest court. It puts the legitimacy of the tribunal in question. The Harper government has no choice but to provide access to information so Quebecers can have the entire truth."
A Harper spokesman said Tuesday the federal government isn't going to revisit history and plans to concentrate on jobs and the economy.
Quebec opposition parties in the legislature have also shown little appetite for addressing the brouhaha.
All provinces except Quebec, which was then led by sovereigntist premier Rene Levesque, endorsed the Constitution in 1982.
Also on HuffPost