The commission said it would announce the results of Zimbabwe's presidential race, pitting President Emmerson Mnangagwa against opposition leader Nelson Chamisa, only after all the votes have come in from across the country.
More than 5.5 million people were registered to vote in an election featuring a record number of more than 20 presidential candidates and almost 130 political parties vying for parliamentary seats.
Riot police used water cannon and tear gas to control chaotic scenes as crowds burned tyres and pelted police vans with stones.
The deployment of soldiers and their beating of unarmed protesters is a setback to President Emmerson Mnangagwa's efforts to shed Zimbabwe's pariah status after decades of repression under Robert Mugabe, who was ousted in a coup in November.
The election commission has said there has been no cheating and it needed time to collate the votes.
Mr. Brok said that ballots for the presidential vote were counted first in polling stations.
The vote attracted a high turnout of 70% and was monitored by worldwide observers.
Parliamentary results early on Wednesday showed Mr Mnangagwa's Zanu PF party cruising to a big majority after picking up 109 seats against 41 for the opposition Movement for Democratic Change (MDC).
Support for Zanu-PF historically has been deepest in rural areas, particularly the party's Mashonaland heartland, where more than two-thirds of Zimbabwe's 17 million people live. "We won the popular vote & will defend it!"
"What they have done is intimidate people in the rural areas saying, "we will kill you if you vote MDC" and so on and then the global observers say this election was free and fair".More news: Hamas, others move to uphold ceasefire with Israel
Election monitors also expressed "concerns about the independence" of the Zimbabwe Electoral Commission (ZEC), reporting that results had not been made public at one in five polling stations....
But it said partial presidential results could be announced later Wednesday.
"They've rigged these elections".
If neither candidate receives an outright majority, there will be a September 8 runoff.
This is the first time in 16 years that the government has allowed European Union and USA election monitors into the country.
The EU observer mission said "a truly level playing field was not achieved" in the election, pointing out the "misuse of state resources, instances of coercion and intimidation, partisan behaviour by traditional leaders and overt bias in state media".
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. They need a good change.
Opposition Movement for Democratic Change (MDC) supporters walk towards the Zimbabwe Electoral Commission (ZEC) headquarters on August 1, 2018 in Harare, to protest against alleged fraud in elections.
A Zanu-PF spokesman dismissed the opposition's allegations of interference, telling the BBC he had "no clue" what Mr Biti was talking about.