He was addressing a media conference in Harare Friday.
Kazembe told the media police were currently busy with attempts to have the politicians brought to justice on Zimbabwean soil.
“We are seized with securing the return of fugitives from justice that are scattered in various parts of the globe.
“Zimbabwe is known for its fair justice system which will afford all such fugitives the opportunity to return home and clear their names,” said the minister.
“As law enforcement agencies, our role is to bring suspects to justice then the normal procedure take effect.
“We urge the suspects to do themselves a favour by voluntarily returning to clear their names if they are innocent.”
Former ministers Jonathan Moyo, Saviour Kasukuwere, Walter Mzembi and Patrick Zhuwao were hounded out of the country after the military dethroned then President Robert Mugabe 2017.
They were close allies of the now late leader who were fiercely opposed to incumbent President (then Vice President) Emmerson Mnangagwa’s take-over bid as the country’s number one.
They have adamantly refused to return home claiming their safety was not guaranteed.
However, government insists the exiled politicians were fugitives from the law and have requested South African authorities to extradite them under existing treaties.
Added Minister Kazembe Friday, “The police are keen to interview the likes of Saviour Kasukuwere, Walter Mzembi and all the others who have cases to answer.
“They are all free to come back into the country and clear their names if they are innocent.”
The former cabinet ministers fled the country after they had been charged with corruption.
In his address, Kazembe also warned social media abusers saying they will not succeed in trying to prevent Zimbabwe’s diplomatic engagement and reengagement efforts.
“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,” he said.
“Let’s be reminded that the peace we are enjoying did not come by accident as there are some among us, some Trojan Horses, working day and night to try to cause chaos in our nation.
“They are trying to subvert our economic revival efforts. They are trying to prevent our diplomatic engagement and reengagement efforts. However, they will not succeed in this anti-people agenda of theirs.”