It says the vote was free and fair and that parliamentary results show that the ruling party won a majority.
The electoral commission said it may take until Saturday-the maximum allowed under the constitution-to declare the presidential victor in Monday's vote, which pitted Mr. Mnangagwa, the longtime strongman's successor against Nelson Chamisa, a lawyer barely half his age.
The ruling Zanu-PF party has won the majority of parliamentary seats.
Tension is rife in Zimbabwe after violence broke out on Wednesday, August 1, following claims by Opposition candidate Nelson Chamisa that the Monday, July 20, election was rigged in favour of President Emmerson Mnangagwa.
A voter in Harare said Zimbabwe was eager to hear the election results as soon as possible.
Several hundred MDC supporters gathered outside the party headquarters in Harare, chanting and shouting that they had won the elections.
Meanwhile, officials from the electoral commission were read the results from the parliamentary contest in a stuffy meeting room in the Rainbow Hotel.
There have been threats of protests and the opposition parties have said they will release their own set of results.
They went on the rampage down Harare's busy streets towards an old Zanu-PF office with large stones, sticks and anything they could grab along the way.
The leader of the opposition, Nelson Chamisa, tweeted that he had "won".
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The military has ruled Pakistan through various coups for almost half of the country's history since independence in 1947. In other areas, it said, "polling staff appeared to be biased toward a certain party", without naming the party.
Speaking in Harare this evening, President Mnangagwa said the hooliganism and violence came as a surprise, adding that the opposition party leadership is to blame.
Elmar Brok, head of the European Union observer mission, said there were "many shortcomings" in the election, but it was unclear whether they influenced the results.
Mr Mnangagwa, a former deputy president who fell out with Mr 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. The electoral commission warned that final results of the presidential first round may not be known until Friday or Saturday.
It suggested there was a deliberate effort to delay announcing the results, reflecting deep suspicion about the panel presiding over the election.
Mr Mnangagwa took over the ZANU-PF party after ousting Robert Mugabe in a bloodless coup in November. "A lot of the protesters I've spoken to say, 'We don't need to see any more".
The EU did not understand why the release of the presidential result was taking so long, he said.
The regional Southern African Development Community bloc, in its preliminary report, said on Wednesday that the campaign and election had "proceeded in a peaceful and orderly manner and were largely in line" in Zimbabwean law.
On Tuesday Former Movement for Democratic Change (MDC) finance minister Tendai Biti and ZESN, the main domestic election monitor, said one in five polling stations - more than 2,000 in all - had not physically posted tallies on their doors, as required by law.
The most important thing for us now is to move beyond yesterday's tragic events, and to move forward, together.I am therefore calling for an independent investigation into what occurred in Harare yesterday.