"It does not deter anyone", he said, adding that no political rallies would be cancelled and urging fellow politicians to "continue to campaign peacefully".
"Let me make it very clear that nothing will stop the elections in Zimbabwe, nothing at all", Vice President Constantino Chiwenga, who was lightly bruised in Saturday's blast, told a rally outside the capital, Harare.
Twenty-three candidates - the highest number in the country's history - will contest the presidential race.
George Charamba tells the state-run Sunday Mail newspaper that the historic July 30 election will go ahead as planned despite the blast that occurred shortly after President Emmerson Mnangagwa addressed a stadium crowd in Bulawayo.
Those policies were cornerstones of Mugabe's near four-decade rule, but the ruling ZANU-PF says Zimbabwe is at a critical stage of its transition and needs an experienced hand like Mnangagwa at the tiller.
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But Trump's frustration over the issue only grew. "What President Trump has suggested here is both illegal and unconstitutional". Trump signaled in his tweet that he doesn't want migrants and asylum seekers to have to be processed through the court system.
"Several people were affected by the blast, and I have already been to visit them in the hospital", Mnangagwa wrote on his verified Facebook account describing the attack as a "senseless act of violence". He has openly joked about them at rallies.
No arrests have been reported. The broadcaster also showed footage of a jovial Mnangagwa walking around the state house gardens in Bulawayo. He added: "I can assure you these are my normal enemies". The country's main opposition leader, Nelson Chamisa of the Movement for Democratic Change, also condemned the attack, saying that any political violence was "totally unacceptable", according to media reports.
The president has vowed to hold a free and fair election, the first since longtime leader Robert Mugabe stepped down in November under military pressure.
One of Zimbabwe's vice presidents is calling Saturday's explosion at a presidential campaign rally "terrorism" and says any candidate who feels "afraid and scared" will receive security.
Previous elections in Zimbabwe have been marred by electoral fraud, intimidation and violence, including the killing of scores of opposition supporters in 2008.