Among those targeted was prominent Zimbabwean investigative journalist Hopewell Chin'ono who is still in police custody after his recent arrest in his home country's capital of Harare on 20 July.
The 49-year-old is accused of inciting Zimbabweans to join a planned anti-government protest during the coronavirus outbreak, News24 previously reported.
"Disturbing reports of violence, intimidation, torture and detention without trial being carried out by the Zimbabwean government against citizens, journalists and opposition voices cannot go unchallenged."
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Maimane said as the leader in the Southern African Development Community (SADC), South Africa could not turn a blind eye, adding quiet diplomacy allowed injustices to continue unabated.
He said President Cyril Ramaphosa, as African Union chairperson, had failed to promote its mandate to promote and protect human rights on the continent.
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Maimane's letter comes after the EFF condemned the action of the Zimbabwean government, calling for tangible interventions and the removal of the Zimbabwean embassy in the country.
"Failure to do this will result in direct action by the EFF to prevent any official of the Zimbabwean government from participating in meetings in South Africa while they wage war on ordinary people in Zimbabwe. Quiet diplomacy by SADC towards human rights violations in Zimbabwe has never worked, and it will not start working now.
"There must be an end to the arrest without trial and victimisation of activists, and all progressive forces must condemn the ZANU-PF government for the brutality it is practicing on the people of Zimbabwe," the EFF said in a statement.