The Rome-based United Nations Food and Agriculture Organisation (FAO) said developing countries which had imported large quantities of cattle, meat or bonemeal from Western Europe were at risk.
The European Commission is considering lowering the age at which cattle must be tested for BSE, from the current 30 months. Germany announced on Friday that it would begin testing all cattle older than 24 months.
In recent months BSE - bovine spongiform encephalopathy - has been identified in cattle in several EU countries which had been regarded as free from the disease.
Suspect EU beef exports
Until now all known cases of BSE and the brain-wasting human variant vCJD (Creutzfeldt-Jakob disease), have been reported in Europe, or in cattle imported from Europe.
But the FAO said "all countries which have imported cattle or meat and bone meal (MBM) from Western Europe, especially Britain, during and since the 1980s can be considered at risk". It said the highest risk was in the Middle East, eastern Europe, North Africa and India.
"There is an increasingly grave situation developing in the European Union, with BSE being identified in cattle in several member-states of the EU which have, until recently, been regarded as free from the disease," the statement said.
BSE first appeared in 1984 in a cow in Britain that was thought to have eaten feed that included offal from sheep that harboured scrapie, a similar illness.
Since then it has spread across much of Europe.
US quarantine
In the UK, more than 170,000 cattle have been diagnosed with BSE and about 1,300 in Belgium, Denmark, France, the Republic of Ireland, Liechtenstein, Luxembourg, Netherlands, Portugal and Switzerland.
Small numbers of cases have also been reported in Canada, the Falkland Islands (Islas Malvinas), Italy and Oman, but solely in animals imported from the UK.
More than 80 people in Europe have died from vCJD.
In Germany, the BSE row led to the resignation of two ministers over their handling of the crisis.
Germany may have to slaughter about 300,000 cows this year to guarantee herds are healthy, as it works to restore consumer confidence in meat.
In Texas, USA, about 1,000 cattle are being quarantined while the Food and Drug Administration (FDA) determines if they ate animal feed from a mill that may have violated rules designed to prevent BSE.
Australia tests
A recent FDA report found that hundreds of feed makers were violating labelling requirements and other rules associated with the ban.
Australia has extended its tests for BSE to dairy and other products from European countries as part of efforts to remain free of the disease.
But in Japan the agriculture ministry said a BSE outbreak was unlikely, as the country had taken sufficient preventive measures.
Officials in Indonesia and Thailand, two other countries pinpointed by scientists as at risk, ruled out any threat, saying they sourced their feed and beef from countries free of the disease.
Indian experts expressed little immediate concern over the disease, though the country has an immense cattle population.
Cows are considered sacred and are protected by Hindus who do not eat beef.