Anti-riot police last week blocked protesting Gukurahundi "survivors" from presenting a petition at the Bulawayo High Court over the 1980s atrocities.
The demonstrators were supposed to start their march at Bulawayo City Hall failed to do so after riot police and plainclothes security details besieged the venue.
Led by Charles Thomas, who was once charged for treason, the demonstrators consequently abandon the march.
Thomas is also a survivor of the Balagwe Gukurahundi torture camp which was set up by government forces in the mid-1980s to target civilians suspected to be Zapu supporters.
"We applied for permission to hold this march, but police declined claiming that we had given them short notice," said Thomas.
"All we wanted was to take our petition to the High Court so that the judiciary can set up an inquest into the Matebeleland genocide.
"There was no point for (President Emmerson) Mnangagwa to set a commission of inquiry into the death of six people in Harare while victims of Gukurahundi like myself are still nursing wounds from the atrocities."
According to the petition, the protestors were also demanding compensation from the government.
"We submit this petition for inquest into the Gukurahundi genocide as survivors of this genocide," read the document in part.
"We demand justice for families of survivors and victims. From 1983-1987, Zimbabwe committed a second genocide and there has been no redress for us.
"We also request compensation, failing which we take this matter to international bodies."
The petition was addressed to the Bulawayo High Court's most senior Judge.
Thomas was arrested alongside exiled Paul Siwela in 2011 for allegedly distributing fliers calling on Zimbabweans to revolt against the government.