"This process is so peaceful. This is what we want and should continue now during the process of campaigning, during the elections, post elections," Mnangagwa said.
"The process is going very, very well, and I'm happy that Zimbabwe is now a mature democracy," he told reporters after lodging his application at a court in Harare.
Zimbabwe goes to the polls on August 23 to elect a president and legislature.
Last week, 39 opposition activists were charged with "demolishing" the offices of the ZANU-PF party, which has been in power since independence from Britain in 1980.
Earlier this month, five opponents were arrested for allegedly assaulting ruling party supporters.
Critics have accused the government of using the courts to target opposition politicians and say there has been an increase in arbitrary arrests and repression.
The opposition has complained about steep hikes in candidacy fees for the presidential elections, which have leapt from $1,000 in 2018 to $20,000 today.
Even so, at least five other figures joined Mnangagwa on Wednesday in submitting their bid for the top job.
Among them was leading opposition leader and Mnangagwa's main challenger, Nelson Chamisa of the Citizens Coalition for Change.
Chamisa said he was confident of beating Mnangagwa in the vote, which is being held in a context of discontent at entrenched poverty, economic hardships and crippling power cuts.
"The greater the challenges, the greater the dimension of our courage, boldness and fortitude to make sure that we win," Chamisa said outside court.
"There's no way Zimbabwe is going to remain the way it is, change is in the air," the 45-year-old lawyer and pastor said.
"Victory is certain."
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