The government blamed the MDC opposition party for inciting the unrest and vowed to enforce a security crackdown, and President Emmerson Mnangagwa said he wanted an independent investigation into the killings and that he is seeking settle differences "peacefully".
Chamisa and Mnangagwa were the main contenders in Monday's vote, the first since Robert Mugabe was forced to resign after a de facto coup in November, after almost four decades years in power. Three people were killed in the election-related violence.
The MDC, which accuses the election authorities of falsifying results, said the army had opened fire "for no apparent reason" leading to the deaths of unarmed civilians.
The Zimbabwe Electoral Commission has said it will announce the results of the presidential race, Thursday.
Zimbabwe's legal and constitutional framework ensured that "key principles for conducting democratic elections such as upholding the right for all political parties to campaign freely and for people to practice their right to cast their votes have been realised", said Augusto.
Even before the violence, European Union observers questioned the conduct of the presidential and parliamentary vote, the first since Mr Mugabe's forced resignation after almost 40 years in charge of the southern African nation.
While the electoral commission legally has five days from the end of the election to announce results, Western observer groups urged the release of the presidential results as soon as possible.
President Emmerson Mnangagwa has said he is in communication with MDC Alliance Presidential candidate, Nelson Chamisa to diffuse the volatile situation in the country saying the dialogue is important to maintain peace in the country.
Officers responded with tear gas and water cannon.
The ruling ZANU-PF party won a majority of seats in Parliament, the Election Commission said.
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The President said the MDC Alliance leadership has to remove its violent supporters from the streets forthwith so that peace returns in the country.
"While we appreciate that the electoral environment was relatively peaceful and a huge turnout at polling stations, we reiterate that electoral processes must always reflect and uphold the true will of the citizens", the coalition said on Wednesday.
This is the first time in 16 years that the government has allowed European Union and United States election monitors into the country.
Chamisa's spokesman, Nkululeko Sibanda, said the army's reaction was unjustified.
Live ammunition was sacked as the Zimbabwe military was brought in to contain the situation.
Chamisa accused ZANU-PF of trying to steal the election.
"The strategy is meant to prepare Zimbabwe mentally to accept fake presidential results". "We won the popular vote and will defend it!" "This time we will not allow it, we will fight", said a protester who wore a red MDC beret in central Harare.
Protesters surrounded vehicles belonging to the observer missions as they passed through downtown Harare.
His Excellency Minister Augusto said that as part of its observation process, the SEOM engaged a wide range of stakeholders including state and non-state actors such as the Government of the Republic of Zimbabwe; Zimbabwe Electoral Commission (ZEC), Political Parties, Council of Chiefs, media, representatives of regional and global organizations, academia, faith-based organizations; and civil society as well as persons with disabilities, women and youth.