Zimbabwe's Covid-19 deaths have passed 1 000 as the country scrambles to contain a spike in infections of the virus that has claimed the lives of three government ministers in the last 10 days.

There are fears the more infectious South African variant of the virus came to the country when thousands of Zimbabweans living in the neighbouring countries returned home for the December holiday.

Zimbabwe has recorded a total 31 320 coronavirus cases and 1 005 deaths. More than half of these have been reported since the beginning of this year, data released late on Sunday showed.

The recovery rate has fallen to 71% from 82% on January 1.

Even before the outbreak of the pandemic, Zimbabwe's healthcare system was facing collapse with workers frequently going on strike to demand better salaries and hospitals facing shortages of medicines and equipment.

Doctors' groups say that hospitals are quickly filling up with Covid-19 patients and that there is an increase in the number of infected people dying at home, unable to afford the steep fees charged by hospitals.

Seeking to re-assure anxious citizens, President Emmerson Mnangagwa said in a national address on Saturday that health experts were assessing different vaccines and would "quite soon" recommend to the government which shots to purchase.

Frontline health workers, who complain that they lack adequate protective clothing, would be the first to receive the vaccine, Mnangagwa said.

Early this month, Zimbabwe extended a nationwide curfew, banned gatherings, closed its land borders and ordered non-essential businesses closed for a month in an effort to curb the surge in coronavirus infections.

The government said it was ready to introduce stronger measures if necessary.