"I feel a deep sense of shame" about South Africa’s refusal to condemn Mugabe, said the group’s honorary president Kumi Naidoo.
"Zimbabweans asked us how can you let us down… after years of solidarity during the struggle" against apartheid.
During a week-long mission to Zimbabwe last month, a Civicus team produced a video with the aim of showing that the country’s reality is "much more tragic" than what is reported by the media.
Zimbabweans interviewed in the video expressed their disappointment with the African Union, the Southern African Development Community (SADC) and the South African government.
"South Africa, SADC, and the African Union have failed the Zimbabwean people," Naidoo said.
"We want SADC and the AU to send a clear message that they will not continue to accept abductions and torture.
"We want them to find a way to ensure that humanitarian aid goes to the people" and to stop recognising Mugabe as president, he said.
Rock concerts to hunger strikes
The organisation, which gathers civic groups from 109 countries, also called for former South African president Thabo Mbeki to step down as mediator in Zimbabwe’s crisis.
Civicus plans to launch an awareness campaign, with activities from rock concerts to hunger strikes, "to put more pressure on the South African gouvernent to significantly change its policy and posture towards Mugabe", Naidoo said.
Millions of Zimbabweans have fled their country’s political, economic and humanitarian crisis, with many coming to neighbouring South Africa, the continent’s economic powerhouse.
Bishop Paul Verryn, whose Methodist church provides refuge for hundreds of Zimbabwean migrants in Johannesburg, said most of the people seeking his care say they fled threats or political persecution, while a minority say they came for economic reasons.