Kathrada spoke to media after casting his vote in the elections which will usher in a fifth democratic-elected government since Mandela became President after 27 years as a political prisoner.
Kathrada served just two years less than Mandela after they were both convicted in the infamous Rivonia Treason trial in 1963.
"We miss him, not only today, but all the time," Kathrada said.
Mandela died in December last year after a long illness.
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"They must exercise their vote. Many people sacrificed their lives to be able to vote and particularly we appeal to the young people because it is their future," he said.
"The policy that (Mandela) was wedded to is firmly in place. Although we miss him, we know President Zuma, and his fellow executive members are carrying out the policy that is laid down by the ANC, the same policy that Madiba and (former) president Mbeki carried out," Kathrada said.
Kathrada became a Member of Parliament in Mandela's government, but now occupies himself mainly with promoting democracy and non-racialism through a Foundation in his name, which is based in the mainly Indian residential suburb of Lenasia, south of Johannesburg.