The row is about whether Vice-President Emmerson Mnangagwa was poisoned earlier this year when he attended one of Mugabe’s rallies.
At the rally, Mnangagwa took ill suddenly and was taken to a clinic in Zimbabwe and then flown by the air force to a hospital in South Africa, where he remained for two weeks.
He made a statement after his return, saying he had not eaten any ice cream made by the Mugabe family’s dairy. The ice cream was distributed to people at the rally.
He also allegedly told Mugabe he had not been poisoned.
But according to local news reports, Mnangagwa claimed at a memorial service for a colleague last week that he had been poisoned.
Vice-President Phelekezela Mphoko issued a statement on Monday, when he was acting president as Mugabe was in South Africa, that Mnangagwa’s alleged statement that he had been poisoned was “calculated to undermine Mugabe's authority and destabilise the country by using lies to fan ethnic tensions for political gain. This must stop, sooner rather than later."