China has pledged to complete by Saturday the slaughter of animals suspected of spreading the Sars virus.
The civets are being placed in cages and destroyed
The government has started killing thousands of civets in the southern province of Guangdong.
Researchers in Hong Kong have linked the virus carried by China's latest Sars patient to a strain found in the cat-like animals.
But the World Health Organization criticised the cull, saying there is no firm evidence that civets carry Sars.
The WHO cautioned that the slaughter - which has seen animals being drowned in disinfectant and then electrocuted and incinerated - might erase clues about how the disease spread, and also risked spreading it.
"If we used knives to kill them, the blood would spread the disease," a Guangdong official told Reuters news agency.
An estimated 10,000 civets in Guangdong are due be disposed of in this way by Saturday.
Civets are small, weasel-like animals considered a delicacy in China's Guangdong province.
Part of mongoose family, distant relative of feline cat
Weasel-like face, cat-like body
Served in wild game restaurants
Estimated 10,000 in Guangdong markets
May have been the source of the virus which jumped to humans
Hong Kong and Taiwan have stepped up their monitoring of visitors from China, which had been Sars-free for six months before the latest case was confirmed on Monday.
In the Philippines, authorities are monitoring 38 people who may have come into contact with a woman who may have become will with the virus in Hong Kong. The woman and her husband showed signs of improvement on Tuesday.
The BBC's Louisa Lim, in Beijing, says that in contrast to the last outbreak more than a year ago, there has been little sense of panic.
People are generally confident that the government has the situation under control, our correspondent says.
The WHO said the slaughter was radical and that the man's case remains an isolated one which does not constitute a public health emergency.
It also warned that not enough research had been conducted into possible links between the civet cat and Sars.
"At this point in time... without seeing that data, there is no conclusive evidence that civets are the animals that carry the Sars virus," WHO Sars team leader Judy Hall told the BBC.
Many researchers believe the strain of Sars which killed hundreds of people last year in China and across the globe could have jumped species to humans from an animal like the civet.
But China's latest case - a male 32-year-old television producer - had claimed not to have eaten any wild animals before he fell ill, although did admit to touching at least one rat.
The man is currently in hospital in the city of Guangzhou in the Guangdong province.
An additional 25 people who had contact with the patient have been isolated, but none appears to be infected.
Sars killed 349 people on China's mainland during the previous global outbreak.