There are fears the rainy season will worsen the outbreak
Zimbabwe has rejected calls for it to declare a state of emergency over a cholera outbreak which has killed more than 360 people since August.
The deputy health minister said the outbreak was under control and blamed the situation on Western sanctions against President Robert Mugabe.
South Africa's health minister said it was "dire" and promised not to block ill Zimbabweans entering the country.
Aid agencies have warned that the death toll could rise with the rainy season.
South African health minister Barbara Hogan said Zimbabweans were neighbours and South Africa would assist them in every way.
She said the Zimbabwean assertion that the outbreak was under control did not reflect the whole country's opinion, particularly as there was no recognised government there.
Her comments came as South African health officials work to stop the outbreak spreading across the border after three deaths in the border town of Musina.
The BBC's southern Africa correspondent, Peter Biles, says reports from across the border in Beitbridge suggest that the Zimbabwean authorities do not have the resources to deal with the situation.
With Zimbabwe's rival parties meeting in South Africa for talks aimed at ending deadlock over a power-sharing deal, Botswana's foreign minister told the BBC that borders with Zimbabwe should be closed to push Mr Mugabe from power.
Earlier, UN chief Ban Ki-moon said Zimbabwe could not afford to fail in negotiating a power-sharing deal if the country was to improve its humanitarian situation.
Mr Ban said President Mugabe's Zanu-PF and the opposition Movement for Democratic Change needed a workable agreement soon, so they could tackle "formidable challenges" ahead.
Dying at home
The number of people being infected with cholera is rising and nearly 9,000 cases have now been confirmed, the United Nations says.
Aid agency Oxfam earlier called on Zimbabwe's government to declare a national health emergency.
It said ordinary Zimbabweans were desperately short of food, health care, clean water and safe sanitation, and the crisis is set to worsen significantly in December.
The economy is in free fall, with inflation last listed in July at 231,000,000%.
"The situation is under control, there is no need to declare it [an emergency]," Zimbabwean Deputy Health Minister Edwin Muguti told AFP news agency on Wednesday.
"These are results of punitive illegal sanctions imposed on us by the West... I am sure they like what they are seeing from this outbreak."
Zimbabwe Doctors for Human Rights believes many people are dying at home where they are not being treated.
The organisation's Dr Douglas Gwadziro said the disease might also start to spread more rapidly now that the rainy season had begun.
There was, he added, a need to deal with the sanitation problems in the urban areas such as the capital, Harare.
Botswana's Foreign Minister, Phando Skelemani, told the BBC's HardTalk programme that the region needed to accept that the mediation in Zimbabwe's political crisis had failed.
"The rest of us should own up and say 'Yes, we have failed'. Call upon the international community and tell Mugabe to his face, 'Look, now you are on your own, we are switching off, we are closing your borders', and I don't think he would last," he said.
"If no petrol went in for a week, he can't last."
In another development, Zimbabwean Central Bank Governor Gideon Gono was reappointed for another five years, the state-run Herald newspaper reports.
Meanwhile, the US government has blacklisted and frozen the assets of four people it says are allies of Mr Mugabe:
- John Bredenkamp, a Zimbabwean businessman
- Muller Conrad "Billy" Rautenbach, a Zimbabwean businessman
- Mahmood Awang Kechik, a Malaysian urologist
- Nalinee Joy Taveesin, a Thai businesswoman.
"The financial and logistical support they have provided to the regime has enabled Robert Mugabe to pursue policies that seriously undermine democratic processes and institutions in Zimbabwe," the government statement said.