The MDC Alliance says the ruling Zanu-PF party has rigged Monday's presidential and parliamentary vote.
The opposition party won in most urban centres. The country's electoral commission said on Wednesday it would set the date for the release of the final results "sometime tomorrow". Numerous protesters tried to get into the National Results Centre (NRC). The 40-year-old vibrant leader says they have "won the popular vote".
Mnangagwa, a former deputy president who fell out with Mugabe and then took over from him, has said his showing in the presidential polls was "extremely positive" while urging people to wait for official results.
Gunfire was heard downtown throughout the afternoon, including near the ruling party headquarters where protesters had gathered.
Opposition MDC party supporters burn election posters depicting Zimbabwean President Emmerson Mnangagwa during the protests.
Automatic gunfire has also been heard and an army helicopter has been spotted in the skies. Several streets were still strewn with rocks and the charred remains of fires.
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"He tweeted: "#InZimHarare a couple people have been injured from the rubber bullet shots. "We need security for the people". "Now is the time for responsibility and above all, peace".
The worldwide community's view on the election is crucial to Harare's efforts to patch up relations after years of hostility under Mugabe and secure the billions of dollars of donor funding and investment needed to rebuild its economy.
It is also reported they have fired water cannons.
But the mood quickly descended into anger as MDC supporters rallied in the city, chanting against the government and burning tyres in the streets.
European Union chief observer Elmar Brok said there were "efforts to undermine the free expression of the will of the electors through inducements, soft intimidation, pressure and coercion... to try to ensure a vote in favor of the ruling party".
Mnangagwa said the violence was meant to disrupt the election and blamed the MDC leadership.
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ZEC chief Priscilla Chigumba said the presidential result may not be ready until Saturday. "We have won this one together". You voted for total Change in this past election!
He said: "We have seen how we have won in those areas including rural areas, we were leading, and now they want to hide on the Zanu PF usual manipulation that they control rural areas". He accused the commission of releasing the parliamentary results first to prepare Zimbabweans for a Mnangagwa victory.
MDC supporters have ripped down a Mnangagwa billboard.
A Harare-based political analyst with Zimbabwe Democracy Institute, Pedzisai Ruhanya, said that the results released so far could be a reflection of the will of the people but were not flawless.
Protests are evolving as fires appear to have been deliberately started in Harare.
More 58 constituencies are yet to be declared, but ZANU-PF only needs 140 seats to the garner the 2/3 majority in Parliament.
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Watching the results trickling in from the Zimbabwe Electoral Commission (Zec) in the early hours, it became apparent that the ruling Zanu-PF would have a majority in parliament. The uncertainty about the results had triggered fears among opposition activists that the government or the military could refuse to cede power if the Zanu-PF was defeated.