Official results show the ruling Zanu-PF party won the most seats in the parliamentary ballot, but the opposition Movement for Democratic Change (MDC) rejected the outcome and claimed there had been fraud.
The EU's assessment is critical in determining whether Zimbabwe can fix its image and attract the foreign investors needed for an economic revival. The ruling party's margin of victory in legislative elections makes Mnangagwa the stand-out favourite in that race, which featured 22 candidates.
The electoral commission warned that final results of the presidential first round may not be known until Friday or even Saturday. "So I have yet to learn why they will be released last", he added, urging the electoral commission to release the results as fast as possible and for each individual polling station.
"We are absolutely confident there was no rigging... we at the Zimbabwean Election Commission will not steal (the people's) choice of leaders, we will not subvert their will", ZEC chair Priscilla Chiguma said a day after the vote.
It alleges that the governing Zanu-PF party has rigged Monday's elections.
If no presidential candidate wins more than 50 per cent of the vote, a runoff will be held September 8. Numerous protesters tried to get into the National Results Centre (NRC).
His opponent Chamisa, however, was not prepared to wait on the release of official results, which he has already derided as fake.
On Wednesday they announced their findings, noting that while the polls were an improvement on previous ones there had been misuse of state resources and media bias.
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But he said that Democrats , not his fellow Republicans, would be the ones targeted. The Black Lives Matter movement was likewise abused by Russian actors in 2016.
Many Zimbabweans looked to the vote as a launching pad for a return to the kind of worldwide acceptance and relative prosperity that the country enjoyed in the first part of the rule of Mugabe, who took office after independence from white minority rule in 1980.
Zimbabwe was once one of Africa's most promising economies but descended into corruption, mismanagement and diplomatic isolation in the latter stages of Mugabe's administration. Its population of 13 million is struggling amid shortages of foreign currency, unemployment above 80 percent and lack of foreign investment.
Basically Zanu PF has won the two-thirds majority and thus has the power to change the constitution if need arises.
Chamisa declared an early victory on Tuesday long before the counting had been completed - including in the rural regions that tend to overwhelmingly support the ruling party.
"There is no good reason why ZEC has managed to announce parlay results but not presidential results per constituency".
MDC-Alliance won all the seats announced in Harare and Bulawayo, while NPF grabbed Kwekwe Central.
The opposition has alleged irregularities, saying voting results were not posted outside one-fifth of polling stations as required by law.
On Wednesday, the European Union addressed the same issue. "They caused massive destruction of property which includes shops and we are now assessing the extent of damage", she said, warning that such acts will be met with the full wrath of the law.