Zimbabwe police say that three people have been killed in the capital Harare as soldiers dispersed stone-throwing opposition supporters who accused the ruling party of trying to rig Monday's presidential election.

Even before the violence, European Union observers questioned the conduct of the presidential and parliamentary vote, the first since former president Robert Mugabe's forced resignation last November after nearly 40 years in charge of the southern African nation.

Zimbabwe's electoral commission had said it would start announcing results for the presidential race from this morning, but that was then pushed back at least 24 hours.

EU monitors said the delay was undermining the vote's credibility.

Police spokeswoman Charity Charamba told state broadcaster Zimbabwe Broadcasting Corporation (ZBC) that the three people killed in the clashes had yet to be identified.

Gunfire was heard as troops, some with their faces masked, and backed by armoured vehicles and a military helicopter, cleared the streets of opposition protesters.

A vendor runs for cover as soldiers clear demonstrators in Harare

The unrest started soon after Nelson Chamisa, leader of the opposition Movement for Democratic Change (MDC), declared that he had won the popular vote.

After burning tyres in the streets, scores of his supporters attacked riot police near the Zimbabwe Election Commission (ZEC) headquarters.

Officers responded with tear gas and water cannon.

"I was making a peaceful protest. I was beaten by soldiers," said Norest Kemvo, who had gashes to his face and right hand.

"This is our government. This is exactly why we wanted change. They are stealing our election."

Mr Mnangagwa said the violence was meant to disrupt the election and he blamed the MDC leadership.

"We hold the opposition MDC Alliance and its whole leadership responsible for this disturbance of national peace, which was meant to disrupt the electoral process," Mr Mnangagwa said, according to ZBC.

Mr Chamisa's spokesman, Nkululeko Sibanda, told reporters the army's reaction was unjustified.

"Today we saw the deployment of military tanks and firing of live ammunition on civilians for no apparent reason."

United Nations Secretary-General Antonio Guterres called on Zimbabwe's political leaders and people to exercise restraint and reject any form of violence.

Justice Minister Ziyambi Ziyambi said the army had been called in to ensure "peace and tranquillity".

Mr Charamba said the troops were deployed at the request of police who could not cope with the violence, and will remain under police command.

As gunfire reverberated through downtown Harare, Mr Mnangagwa called for calm and urged patience while results were collated.

Many protesters accused the army of unprovoked brutality.

EU observers voiced concern about delays in releasing the results of the presidential contest, a two-horse race between Mr Chamisa and Mr Mnangagwa, head of the ruling ZANU-PF party.

Without the international community's stamp of approval for the election, Zimbabwe's next leader will struggle to unlock the billions of dollars of international donor finance needed to get the shattered economy back on its feet.

With three seats yet to be declared in the parliamentary contest, ZANU-PF has 144 seats compared to 61 for the MDC, meaning the ruling party achieved the two-thirds majority that permits it to change the constitution at will.

Mr Chamisa said the early release of the parliamentary results was a deliberate ploy to prepare Zimbabweans for a victory by Mr Mnangagwa, a former national security chief nicknamed "The Crocodile" and commonly referred to by the initials ED.

"The strategy is meant to prepare Zimbabwe mentally to accept fake presidential results. We've more votes than ED. We won the popular vote (and) will defend it," Mr Chamisa said on Twitter.