Chamisa made the threats when he launched the alliance's Plan and Environment for a Credible Election in Zimbabwe (Peace) document which outlines the coalition's 10 electoral demands in Harare yesterday.
He said Mnangagwa has been given a window to reform the electoral ground, but appears reluctant to level the playing field.
Chamisa said he would soon mobilise activists to take to the streets if the reforms are not implemented before elections set for July this year.
"This election is going to produce one outcome, and this is victory for the MDC Alliance, we are not going to allow them (Mnangagwa and his government) to reverse the will of the people," Chamisa said.
"In fact, we have given them a window to reform. If they don't, we are going on the streets. We are going to mobilise the people and this is not going to be an MDC Alliance issue, but a people's issue because the issue of resolving governance crisis, social-economic and political question is tied to the issue of free and fair elections.
"We will tell the people that in order to unlock the jam in the country, we have to hold free and fair elections and this is when we count on you (the people) and Mr Mnangagwa, we are going to be your guest soon if those issues are not resolved."
Since he came into power last November, Mnangagwa had been spared protests by opposition activists who believed he was committed to his reform pledge.
Last year, opposition parties under the National Election Reform Agenda held nationwide protests that ended up violent as they demanded former President Robert Mugabe to step down for refusing to reform the electoral roadmap.
Before launching the Peace document, Chamisa and his MDC Alliance partners met an eight-member European Union electoral preparatory team to apprise them on the electoral environment.
Chamisa who is MDC-T and MDC Alliance presidential candidate told the EU team that he had written to Mnangagwa to implement electoral reforms and level the political playing field to enable the country to hold free and fair elections.
The MDC is also demanding an immediate end to the abuse of traditional leaders to play a partisan role, allowing of international observers well before the election date, permission for diaporans to vote, among others.
Chamisa also raised concern over the mysterious departure of former chairperson Justice Rita Makarau and her successor Justice Priscilla Chigumba's recent controversial trip to Russia in the company of Zanu-PF politburo member Christopher Mutsvangwa.
"It is a serious and vicious assault on the integrity and autonomy of ZEC that the electoral management body's new chairperson had undertaken a trip to Russia with a politburo member of Zanu-PF and advisor to one of the candidates in the forthcoming election," Chamisa said.
Meanwhile, acting Information minister Simon Khaya Moyo said Mnangagwa would soon meet leaders of different political parties to discuss different electoral issues, including access to the media.
He made the remarks while addressing legislators in the National Assembly yesterday.
Buhera West legislator Oliver Mandipaka had asked Moyo to explain policies that government had put in place to guarantee journalists' safety in their line of duty, especially at campaign rallies.
"It was recently announced that the President will meet all leaders of political parties, and this is where we want to ensure that all people will have access to the media," Moyo said.
"I want to also believe that when the time comes whoever wins will be cognisant that he or she is responsible for media or other freedoms.We want to be certain that we abide by what has been pronounced by the President, and let us sing from the hymn book of non-violence," he said.
Magwegwe MP Anele Ndebele then quizzed Moyo why his ministry only issued radio licences to State-linked entities.
"Recently the ZBC got another radio licence to open a new radio station (Khulumani FM) in Bulawayo and it is yet another Zanu-PF mouthpiece," Ndebele said.
But, Moyo said no political party owned radio stations in Zimbabwe, and challenged the MP to prove the claims.
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