Mnangagwa's conciliatory remarks came a day after soldiers occupied the streets of Harare, shooting live rounds and beating demonstrators, many of whom were throwing rocks and setting fires to protest alleged fraud in Monday's election. At least three people are killed.
The activists are denouncing violent protests but calling the government's reaction illegal and "grossly disproportionate to the violence that it sought to contain".
The riots surged up to the fence of the Rainbow Towers Hotel & and Conference Centre, where the electoral commission has been announcing results and many global election observers are staying.
Mr Mnangagwa, whose ruling Zanu PF party yesterday claimed a large majority in disputed parliamentary elections, said he had been in contact with the leader of the opposition MDC Alliance in a bid to defuse tensions.
The head of the Commonwealth election observers in Zimbabwe is condemning what he calls the "excessive use of force against unarmed civilians" by security forces.
Even though the election passed off peacefully, several water cannon trucks patrolled outside the central Harare headquarters of the MDC as its red-shirted supporters danced in the streets.
"We are exhausted of them stealing our votes".
Masocha said the MDC Alliance supporters presumed victory for their leader based on false impression that Chamisa had countrywide support, when in reality, it was confined to the capital Harare, where it swept out the ruling Zanu-PF party.
Harare, Zimbabwe: on 1st August 2018, the Head of the SADC Electoral Observation Mission (SEOM) to the 2018 Harmonized Elections in the Republic of Zimbabwe, His Excellency Manuel Domingos Augusto, Minister of External Relations of the Republic of Angola released the Mission's Preliminary Statement, at a press conference held at the Rainbow Towers Hotel, Harare, Zimbabwe, regarding the 30 July 2018 Harmonized elections that represented a political milestone in Zimbabwe's history.
"The more the presidential vote is delayed, the more it calls into question the population's confidence in the election process", said former Liberian leader Ellen Johnson Sirleaf, the lead observer of a United States monitoring mission.
African observer groups said the vote was peaceful, orderly and largely in line with the law but they raised concerns about bias of state media and the commission.
"We are obviously very pleased that the results announced by ZEC so far show that we achieved two-thirds majority from the parliamentary election", ZANU-PF's legal secretary is Paul Mangwana told reporters, referring to the electoral commission.
The election stands as an important test for Zimbabwe as the country tries to rebuild its economy and worldwide standing after almost four decades of Mugabe rule.
Earlier the ZEC said it was still not ready to release the presidential results, but it would know later on Thursday exactly when those results could be made public.
The government warns candidates they face prosecution and jail for prematurely announcing results.
The situation in the country now is rather disappointing, according to many observers.
The ruling party forced Mugabe to resign in November, when the military briefly seized control of the country, and replaced him with Mnangagwa, his former deputy and spy chief. The EU mission questioned why presidential votes were counted first but were being announced last.
He accused Zanu-PF of trying to "manipulate" the results, called V11 forms.