The party's ten provinces, the Women's League and the Youth League have endorsed First Lady Grace Mugabe to be the party's female vice president and to replace Mnangagwa.
Chiwenga made his comments a week after Mugabe fired Chiwenga's ally, Emmerson Mnangagwa, 75, as vice president and expelled him from the ruling party.
Zimbabwe's ruling party described criticism of its conduct by armed forces commander Constantine Chiwenga as "treasonable" and meant to incite insurrection in the southern African nation, deepening the split between the military and 93-year-old President Robert Mugabe.
Both Zimbabwean President Robert Mugabe's famous "blue house" and the Zimbabwean Broadcasting Corporation (ZBC) has been sealed off by heavily armed military personnel, Khuluma Afrika is reporting.
"Please continue with your lives and face up to your own problems", tweeted the country's ruling party, the Zimbabwe African National Union Patriotic Front (Zanu-PF).
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"We must remind those behind the current treacherous shenanigans that, when it comes to matters of protecting our revolution, the military will not hesitate to step in", Chiwenga said in a statement read to reporters at the news conference.
In his statement, Chiwenga said the wanton dismissal of party members must be stopped with immediate effect.
Historically President Mugabe is generally afraid, and interprets any show of defiance as risk of a possible coup and has in the past tightened his personal security over simple things like social media dissent, or strikes by workers.
"Defending the revolution and our leader and president is an ideal we live for and if need be it is a principle we are prepared to die for".
"We very rarely see tanks on the roads", Derek Matyszak, an analyst at the Pretoria-based Institute for Security Studies, told AFP. Her image has been tarnished after an alleged assault on a model she had found in the company of her sons in a luxury apartment in Johannesburg in September. The country is struggling to pay for imports due to a shortage of dollars, which has also caused acute cash shortages.