Suspended national police national commissioner Riah Phiyega cannot be made to shoulder all the blame for the Marikana massacre, Cope said on Sunday.
"All of us know that the massacre at Marikana was too big to lay at the door of one person," Congress of the People's spokesperson Dennis Bloem said in a statement.
"It can't be that Riah Phiyega alone must take the fall."
Instead, Cope suggested that the roles of Deputy President Cyril Ramaphosa – who at the time was a shareholder at Lonmin - and then police minister Nathi Mthethwa, needed further investigation.
In 2012, 34 mine workers at Lonmin's platinum mine were killed – some shot at by police while they were running away – while protesting for higher wages.
On Sunday, City Press newspaper reported that the board of inquiry into Phiyega's fitness to hold office recommended her dismissal.
The Democratic Alliance subsequently also weighed in in this finding, suggesting that the report into Phiyega be tabled in Parliament.
"The DA will write to the chairperson of the Portfolio Committee on Police, François Beukman, to urge that he request for the finalised report from the Claassen Inquiry into the fitness to hold office of the ... Phiyega, to be tabled before Parliament," said DA MP Zakhele Mbhele in a statement.
According to the City Press, the final report has been ready since November 13 this year.
Mbhele said while her party welcomed the finding that Phiyega was unfit for her role, "we maintain that the terms of reference of the inquiry should have been widened to include all of Phiyega's failings during her tenure" in order to ensure a comprehensive conclusion.