State-run newspaper The Sunday Mail quoted Vice President Constantino Chiwenga as saying "we believe we have lost about 13" in the mine disaster, which happened on Friday in the gold-rich town of Chegutu, about 100 kilometers (60 miles) west of the capital, Harare.
Eight have been confirmed dead, with three bodies removed from the mine and five located but not yet removed, Chiwenga said.
He said 21 out of 34 miners believed to be underground at the time of the collapse had been rescued. The remaining five people were presumed dead.
Chiwenga was speaking Saturday at a meeting of the ruling ZANU-PF party, The Sunday Mail reported.
The collapse happened at a disused German-owned mine that had not been properly sealed off, allowing unofficial artisanal miners to find their way in to search for any deposits left over, the vice president said.
Incidents of mine collapses, often involving artisanal miners, are common in the southern African country that is rich in gold, coal and diamonds. Zimbabwe also has Africa's largest reserves of lithium, a mineral in global demand due to its use in electric car batteries.
Zimbabwe's mineral-rich national parks, abandoned mines, rivers and even towns are often swarmed with people, including young children, seeking to find valuable deposits. It is one of the few economic activities still going on in a country that has suffered industry closures, a currency crisis and high unemployment over the past two decades.
Critics blame economic mismanagement and corruption for the collapse of a once-thriving economy and one of Africa's bright spots. The government points to two decades of sanctions imposed by the United States over allegations of human rights violations by the government.
Also Friday, Indian businessman Harpal Randhawa and his son were among six people who died in a plane crash near a different diamond mine, according to the same report in The Sunday Times. The small plane reportedly belonged to Randhawa's RioZim mining company. The crash killed everyone on board, the report said.
RioZim was previously part of the British-Australian mining group Rio Tinto.
Chiwenga said the Zimbabwean victims of both tragedies would receive state-assisted funerals, while President Emmerson Mnangagwa called for a moment of silence for those who had died during the ruling party meeting.
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