Omar, born to parents who migrated from Gujarat, had been an activist all his life before he succumbed to cancer in 2004 at the age of 69.
As a lawyer, he was renowned for having assisted political detainees in the apartheid era at no cost. Omar was often detained without trial for opposing the white minority government.
After Thabo Mbeki succeeded Mandela as President, Omar became Minister of Transport.
The Minister of Justice and Constitutional Development, Jeff Radebe, officially opened the new service point of the Cape Town Master of the High Court.
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"The late Omar fought tirelessly for justice in an unjust legal system during the apartheid era and during his tenure as the Minister of Justice he played a major role in setting up the new prosecution system headed by the National Director of Public Prosecutions.
"Omar was also instrumental in the development of the framework for the transformation of the administration of justice," it said.
Among his major achievements was initiating the Truth and Reconciliation Commission, which was established to heal the wounds of apartheid.
"As envisaged by stalwarts such as the late Omar, the relocation of the Masters' office will enable the department to realise the vision of equitable and dignified justice services," Radebe said.