Government has declared it will not return Zapu properties confiscated before the advent of the 1980s Gukurahundi genocide in Matabeleland and the Midlands.
Former guerrillas of Zipra, the armed wing of Zapu, say the government grabbed more than 20 Zapu properties countrywide, among them farms and buildings.
These include Magnet House in Bulawayo, which now houses the Central Intelligence Organisation offices.
Last year, Zapu officials petitioned President Emmerson Mnangagwa to release government's grip on the properties, but there has been no movement on the government side.
Justice minister Ziyambi Ziyambi this week told the Zimbabwe Independent the properties now belonged to government.
"First of all, let me state that I have personally not seen any petition to the effect of demanding any Zapu properties. Yes, I have heard and read that some people claim to have petitioned my office and that of the president over those said properties," Ziyambi said.
"Secondly, we come to legal issues covering such an issue. Legally speaking, there is no party called Zapu. Which one is the one you are talking about? The Zapu which existed prior to 1987 joined hands with Zanu PF to become one party.
"It goes without saying, therefore, that any property that belonged to either party before that Unity Accord of 1987 automatically belongs to Zanu PF."
Dumiso Dabengwa, a former Zanu PF politburo member, is the leader of the revived Zapu. Dabengwa was the Zipra intelligence supremo during the liberation war.
Ziyambi said in the event that there were persons who felt hard done by the declaration, they were free to approach the courts to compel the government to release the properties.
In his opinion, such an effort would hit a dead end as the courts would dismiss the applications, he added.
"No one can motivate such an issue even in courts of law because they will lose such a case. The only party that can say anything with regards to these so-called properties is Zanu PF because they are the legal owners of those properties following the 1987 Unity Accord," he said.
Zapu's petition read in part: "Mr President, following your inaugural speech at the National Sports Stadium, in which you spoke so glowingly of a new dispensation and a new era, where rights of every citizen are respected and promoted, we write to remind you of a major violation of our rights as Zapu and Zipra by the government of Zimbabwe, which you now lead.
"The actions by government on Zapu and Zipra, especially around the above matter, infringes on equality and belonging to the country as bona fide and equal citizens.
"We have been making calls for this overdue process, albeit on deaf ears. In anticipation and trust that you will walk the talk on your promise to respect and promote people's rights, we hope to receive from your government what duly belongs to us."