Chamisa, a lawyer and pastor who leads the opposition Movement for Democratic Change party, has claimed victory based on results supporters said they collected from agents in the field. "It is so obvious that rigging has taken place since Monday".
With elections under Mugabe marred by fraud and often deadly violence, his successor Mnangagwa, 75, had promised a free and fair vote and invited global observers.
"I am not happy because at the polling station where I voted most of the people were voting for MDC alliance but if you see the results of the constituency it does not reflect the will of the people".
Zimbabwe's ruling Zanu-PF party won the most seats in Parliament, official results showed Wednesday, as the opposition Movement for Democratic Change (MDC) Alliance protested against alleged widespread fraud and the count continued in the key presidential race.
The news was delivered by the Zimbabwe Electoral Commission (or ZEC) as they announced the results in dribs and drabs for the lower house of parliament.
MDC-Alliance is led by Mr Nelson Chamisa who on several occasions posted messages on social media saying he would not accept any result in which he was not the victor.
The security forces opened fire with guns, water cannons and tear gas, and protesters burned cars and threw rocks as helicopters hovered above Harare.
"It's a clear attempt by ZEC to subvert the will of the people".
The man died after soldiers fired live ammunition during opposition protests in downtown Harare, AFP reporters saw. We've more votes than ED (Emmerson Mnangagwa). We know what's happening here.
Scores of his supporters who had been burning tyres in the streets then attacked riot police near the Zimbabwe Election Commision (ZEC) headquarters.
The unrest bodes ill for a country that has suffered multiple violent election cycles. The outcome will have far-reaching implications for the African nation whose economy and infrastructure have suffered during the almost four-decade reign of Mr Mugabe.
Amnesty's acting secretary general Colm O Cuanachain said in a press release that the "militarisation" of the election aftermath "is muzzling freedom of expression, association and assembly".
The candidates' competing claims following the first elections since former president Mugabe was ousted in November raise the prospect of fraud allegations and a possible run-off vote on September 8.
This was the first time western observers were allowed to monitor the democratic process in Zimbabwe for nearly two decades.
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 worldwide election observers are staying. Mr Chamisa tweeted on Wednesday. "Now is the time for responsibility and above all, peace". "Zimbabwe's main problem is a confidence crisis & these fictitious election results does not alley such fears", added Chimhutu. "We won the popular vote (and) will defend it", Chamisa said on Twitter. "We have won this one together".
A Harare-based political analyst with Zimbabwe Democracy Institute, Pedzisai Ruhanya, said the results released so far could be a reflection of the will of the people but were not flawless.