Forty-nine people were injured, Charamba said.
The explosion at a campaign rally for Zimbabwe's president that injured 49 people will not delay next month's historic election, officials said Sunday, as a vice president called the attack "terrorism" and said any frightened candidate would be provided with protection.
Mnangagwa - who took power after Mugabe's ouster in November - said he was the target of the attack, which the state media is describing as an assassination attempt. Witnesses said several people were injured, including a vice president.
Chipo Dendere, a Zimbabwean professor of political science at Amherst College in the USA, said the incident would change the tone of the election campaign.
While Bulawayo has always been a bastion of opposition to the ZANU-PF and it was Mnangagwa's first rally in the city, commentators suggest the attack could have been sparked by internal party ructions.
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Zimbabwe's polls will be held in the presence of Western observers for the first time since 2002.
In an audio message to the country, Mnangagwa condemned the bombing and vowed to press on with his government's political and economic reform drive. "While we have all chosen the path of peace others, unfortunately, still cling to the tools of violence".
He has pledged to hold free and fair elections as he seeks to mend global relations and have sanctions against Zimbabwe dropped. Dramatic footage showed him walking off the stage and into a crowded tent where the blast occurred seconds later, sending up smoke as people screamed and ran for cover. Unlike the past elections that were marked by killings, internal displacements, destruction of property and systematic intimidation of mainly opposition activists, this time around the country's politics had taken a somewhat mature route - allowing for all political actors to freely solicit for votes even in the so-called "no-go areas" without fear.
Zimbabwe police spokeswoman Charity Charamba said "comprehensive investigations are in progress" into the blast.