Addressing the media in Harare on the state of the security situation in Zimbabwe, Kazembe said the two ex-ministers who were close to the late Robert Mugabe, must come home and have their cases dealt with by the courts.
"We call upon fugitives who have fled the country to come back voluntarily and clear their names. The police are keen to interview them," he said.
Kazembe said Kasukuwere, who was the Zanu-PF political commissar before the downfall of Mugabe in 2017, is among the wanted fugitives who are tarnishing Zimbabwe's image outside the country.
"The abuse of social media and the scourge of fake reportage, which are often motivated by subversive intentions will remain closely monitored to protect peace and stability in the country," Kazembe said."We want to assure the nation that law enforcement agents are alert and the peace prevailing in the country will be guarded appropriately and jealously,"Kazembe vowed.
However, Kasukuwere fired back at the minister saying he had no case to answer.
Kasukuwere immediately took to the micro-blog Twitter responding to Kazembe and several posts demanding why he was supposed to come back to Zimbabwe.
"Clear us out of existence I guess!"
Kasukuwere and Mzembi are in South Africa after fleeing the country at the time they had criminal cases at the magistrate court.
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