However, it said national veterinary services should monitor animal populations for signs of respiratory disease, and conduct appropriate testing.
Influenza is a disease of humans, birds, horses, pigs, and, to a far lesser extent, cats and dogs. The current A/H1N1 virus is reported to contain genes from pig, bird, and human strains of the virus.
The last update from the World Health Organisation (WHO), issued on July 6, showed 94,512 confirmed cases worldwide in 122 countries, with 429 deaths.
However, it is likely that millions of people have already caught the disease, which causes comparatively mild symptoms in healthy people. Disease experts have said the numbers of laboratory-confirmed cases are now largely meaningless.
The WHO announced late last week that it would stop issuing global tables showing the numbers of confirmed cases for all countries.
"The increasing number of cases in many countries with sustained community transmission is making it extremely difficult, if not impossible, for countries to try to confirm them through laboratory testing," it said.
The World Organisation for Animal Health, in its latest guidance, said national veterinary services must ensure a high level of awareness in monitoring animal populations for clinical signs of respiratory disease, and use appropriate testing.
"Should the presence of the 'pandemic H1N1 2009 virus' be detected on a farm, the holding should be subject to an officially developed surveillance plan and movement restrictions applied until recovery."
It said the culling of pigs will not help to guard against public or animal health risks presented by the virus. "As for any other disease, slaughtering of sick pigs for human consumption is not recommended."
However, it stressed: "There is no evidence at this time that animals are playing any role in the epidemiology or the spread of the virus.
"Public and animal health experts worldwide continue their joint effort on scientific research aimed at better understanding the virus and providing sound and science-based recommendations for its prevention and control."