"We are however seriously concerned about evidence of interference. there is a deliberate delay in announcing the results".
Early results from the elections - presidential, parliamentary and local - are expected later on Tuesday, and full results are due by Saturday.
Election officials are counting ballots and both front-runners await the results.
Asked on the credibility of the elections, Justice Chigumba said she is "absolutely confident that the elections were not rigged and we want to show the world that we won't steal or subvert the will of the people".
Winning resoundingly... We now have results from the majority of the over 10 000 polling stations.
Vote counting at a polling station in Bulawayo, Zimbabwe, on Monday.
"It is our view that the high voter turnout is indicative of sound voter education and publicity", said Zimbabwe Electoral Commission (ZEC) chairwoman Priscilla Chigumba at a media briefing in Harare.
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"Concerns still remain about the independence of the ZEC amid executive interference in key electoral processes", Andrew Makoni, the chairman of the network, which deployed about 6,500 observers, said in Harare on Tuesday.
If required, Zimbabwe's 5.6-million registered voters would be asked to return to the polls to vote in a presidential run-off on September 8.
Western election observers were in Zimbabwe, a sign of a freer political environment since the resignation of Mugabe, who declared he would not vote for the ruling party he long controlled and called Chamisa the only viable candidate.
Under Mugabe, elections were often marred by violence, harassment and irregularities.
"By the end of the day today we should be very clear as to an emphatic voice for change, the new, and the young - I represent that", Chamisa said as he voted in Harare, surrounded by vocal supporters. Mnangagwa, the former vice president, was sworn in as Mugabe's successor.
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.