The party called on the Office of the Chief Justice to ensure remaining sensitive information is secured "and mitigate against any efforts to undermine or compromise the dispensing of justice as a result of the break in".
With a total of 15 computers containing confidential information of all the South African judges, judiciary staff and all the courts stolen, it is clear that this was not a random occurrence, and this can be seen as an act of intimidation.
The burglary came just about two weeks after a $15 million heist at the OR Tambo International Airport.
Office of the Chief Justice spokesman Nathi Mncube confirmed the break-in.
The break-in "constitute a huge setback for the entire administration of the justice".
The Office of the Chief Justice was burgled in the early hours of Saturday morning in Midrand.
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The Police's Athlenda Mathe says the task team includes detectives, forensic analysis experts as well as crime intelligence experts.
He added that he would sanction a security assessment to advise on the improvement of security at the offices.
"The break-in was reported to the South African Police Services (SAPS) and various units from SAPS were dispatched to the OCJ to conduct further investigations".
"Targeting the Office of the Chief Justice however is a direct assault on the sanctity of the institutions we, as South Africans, hold dear as propping up our Constitutional order".
ANC also called on law enforcement agencies to ensure that the criminals were dealt with.