The UN has warned the total number of cases could reach 60,000
The latest figures from the UN and Zimbabwe's health ministry reveal that two-thirds of the victims of the cholera outbreak have died this month.
The death toll at the end of last week stood at 1,564, with 29,131 suspected cases since August, the UN said.
Figures from the health ministry on 1 December put cholera deaths at 484.
The UN has warned it could take six months to control the outbreak that has been fuelled by the collapse of the health, sanitation and water services.
According to the World Health Organization, cases have been reported in all 10 of Zimbabwe's provinces.
CHOLERA FIGURES SINCE AUGUST
Cases: 11, 735
Cases in December 68%
"The overall Case Fatality Rate (CFR) has risen to 5.7% - far above the 1% which is normal in large outbreaks - and in some rural areas it has reached as high as 50%," the WHO said in a statement.
Last Tuesday, Unicef put the number of cholera deaths at 1,174.
Aid agencies say so many clinics and hospitals have closed that large sections of the population have no access to medical care.
The suburb of Budiriro in Harare's capital, has been worst hit by the outbreak, followed by Beitbridge on the border with South Africa.
South Africa has recorded 1,279 cases and 12 deaths - the bulk of these in the border region, the WHO says.
Over the weekend, Save the Children said some five million people in Zimbabwe - or about 50% of the country's population - were now in need of food aid.
President Robert Mugabe has been facing intensified criticism over the dire economic and humanitarian situation in Zimbabwe.
He signed a power-sharing deal with his rival, Morgan Tsvangirai, in September, intended to rescue the collapsing economy but progress has since stalled over who should control key ministries.
Mr Tsvangirai has threatened to pull out of power-sharing talks unless abductions of his supporters stop.
According to his Movement for Democratic Change, about 40 human rights activists and opposition supporters have been abducted in the past two months.
Meanwhile, the US envoy to Africa, Jendayi Frazer, has warned that last week's military coup in Guinea should serve as a warning of what could happen in Zimbabwe, if Mr Mugabe is allowed to cling to power and die in office.