Three people died and scores of others were injured on Wednesday when protesting opposition supporters clashed with army and police in the capital Harare.
Police spokeswoman Charity Charamba confirmed the deaths in the violence which also left property destroyed.
She warned leaders of the opposition MDC Alliance against inciting its supporters to engage in violent activities.
Scores of opposition supporters took to the streets of Harare to protest against the delay in the announcement of the presidential election results, as well as alleged rigging of the vote.
"The police condemns in the strongest terms acts of vandalism and hooliganism that occurred in Harare. As investigations continue, we urge members of the public to remain calm and peaceful and not to be persuaded or coerced into engaging in acts of violence," Charamba said.
She said police were keen to interview leaders of the MDC Alliance in connection with the deadly protests.
President Emmerson Mnangagwa, meanwhile, called on Zimbabweans to remain calm and peaceful as the nation awaits the announcement of all election results.
He blamed the MDC Alliance leadership for causing the protests.
"The incidents of violence and hooliganism which broke out in the afternoon came as a complete surprise," he said.
"We hold the opposition MDC Alliance leadership responsible for this disturbance of national peace which is meant to disrupt the electoral process. We hold the party and its leadership responsible for any loss of life, injury or damage to property which arises from political violence which they have aided and abated."
Nkululeko Sibanda, the spokesperson of the MDC Alliance president Nelson Chamisa said the party regretted the deaths during the protests and criticized the security forces for using excessive force to quell the protests.
Chamisa claimed on Tuesday that he had won the presidential poll and said his party will not accept a result to the contrary.
The Zimbabwe Electoral Commission said results for the presidential poll are expected by 4 August.
According to the results declared by ZEC, the ruling ZANU-PF party won a parliamentary majority in the Monday elections. - Xinhua