Movement for Democratic Change (MDC) say Chamisa, 40, has beaten President Emmerson Mnangagwa and his ruling ZANU-PF, "beyond reasonable doubt" after conducting its own count.
Official results strengthened President Emmerson Mnangagwa's prospects of holding on to power in the key presidential vote, showing that ZANU-PF had easily won the most seats in the parliamentary ballot. Two additional parties also received one seat each and 58 of the total 210 were still to be announced.
The general election follows the ousting of long time Zimbabwean leader, Robert Mugabe in November previous year by the military.
The electoral law says the representatives can object to that documentation, but that will not prevent ZEC from releasing the result.
The electoral commission had said it would start announcing results for the presidential race from 10:30 GMT, but this was delayed as commissioners read out more parliamentary results.
But it said partial presidential results could be announced later Wednesday.
'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, Harare.
Zanu-PF saw strong results in rural areas.
African observer groups said the vote was peaceful, orderly and largely in line with the law but raised concerns about bias of state media and the commission.
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Several hundred MDC supporters crowded around the party's headquarters Wednesday and started marching toward the electoral commission after Mr. Chamisa declared himself the victor. They believe the election has been stolen, and are demanding the MDC be announced as victor.
Live video by The Associated Press from Harare shows smoke rising from burning vehicles and opposition supporters scattering after they protested alleged manipulation in Monday's election.
If no presidential candidate wins at least 50 percent of the ballots cast in the first round, a run-off vote is scheduled for September 8.
The European Union, which has been monitoring the elections for the first time since 2002, will issue its verdict later on Wednesday.
The election stands as an important test for Zimbabwe as the country tries to rebuild its economy and worldwide standing after almost four decades of Mugabe rule.
Analysts have said it was unclear whether the country's generals, who ousted Mugabe and ushered Mnangagwa into office, would accept a win by the Movement for Democratic Change (MDC). It has five days from Monday's vote to release them.
More results are expected soon with Presidential election outcome expected by midday today.
Mr Mugabe had voted in the capital of Harare alongside his wife Grace, following a surprise news conference in which he called on supporters to reject ZANU-PF, his former party.
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