Both President Emmerson Mnangagwa and main opposition challenger Nelson Chamisa have expressed optimism about the results, and Chamisa's supporters are already claiming victory based on what they say are results collected from agents in the field nationwide.
A total of 23 candidates across 55 parties are running for the presidency.
Nearly 5.7 million registered to vote in the election that had 23 candidates vying for the presidency and 130 political parties running for Parliament and council.
Winning resoundingly... We now have results from the majority of the over 10 000 polling stations. The victor needs more than 50 percent of the vote to win outright and avoid a run-off in September.
Western election observers were in Zimbabwe, reflecting a freer political environment since the November resignation of Mugabe, who had ruled since independence from white minority rule in 1980.
In Harare 75% of the votes have been finalised while in Manicaland 56%, has been completed.
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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.
There remained concerns about bias in state media coverage of the election, a lack of transparency in ballot printing and reports of intimidation by pro-government local leaders who are supposed to stay neutral. The peaceful election was a break from votes marred by violence.
This comes after Zec acting chief elections officer, Utoile Silaigwana confirmed that the MDC Alliance presidential candidate had been reported to the police for holding an illegal press conference on Sunday at Meikles Hotel after the deadline for political campaigns. Under Mnangagwa, Zimbabwe has said it wants to rejoin the group.
The commission said it would delay releasing any results of the presidential race until all the votes are collated.
It also found the final voters' roll was released too late to analyse it, the electoral commission dispatched more voting kits to rural areas than urban ones and the electoral laws had not been harmonised with the constitution.
"I think the best thing is they got to announce the results as early as possible so that everyone will be settled", said 65-year-old voter Chaka Nyuka in the capital of Harare.