The ruling party has unveiled a draft law that strips voters of the chance to elect the president.
President Mnangagwa's term in office is due to end in 2028 but a bill could open the way for him to extend that time.
President Mnangawa says he wants improved relations, days after Donald Trump said the US would impose an 18% tariff on Zimbabwe.
A total of 95 people are charged with promoting "public violence" and for "breaches of peace".
Many streets across Zimbabwe remained deserted and empty on the day of a planned protest.
It comes ahead of planned protests by a group of war veterans who want Emmerson Mnangagwa to resign.
Zimbabwe's leader faces a backlash from key allies over efforts to extend his time in office.
Amnesty International hails the decision as a "beacon of hope for the abolitionist movement".
Nelson Chamisa, who came second in elections last year, says his party has been "hijacked".
