"The continuing international economic downturn means less money is available for prevention of H5N1 bird flu and other threats of animal origin," Juan Lubroth, chief veterinary officer at the Food and Agriculture Organisation (FAO), said in a statement.
"Even though everyone knows that prevention is better than cure, I am worried because in the current climate governments are unable to keep up their guard," he was quoted as saying.
The Rome-based agency warned large reservoirs of the H5N1 virus still exist in parts of Asia and the Middle East where the disease has become endemic.
"Without adequate controls, it could easily spread globally as it did at its peak in 2006, when 63 countries were affected," the agency said.
The virus killed more than 300 people between 2003 and 2011, as well as forcing the culling of 400 million domestic chickens and ducks and causing an estimated $20 billion (15 billion euros) in damages.
The FAO also cautioned of the growing threat from Peste des Petits Ruminants, or PPR, a highly contagious disease that affects sheep and goats.
FAO said the virus, for which a vaccine exists, had wrought havoc in the Democratic Republic of Congo and was spilling over into southern Africa.
Among the prevention measures against animal diseases recommended by FAO are improved general hygiene, market and border controls and health inspections in farms and markets, as well as equipment and training for laboratories.