The World Health Organization has warned against panic-buying stocks of a drug thought to work against the virus.
Greece is the first EU member to confirm a case of bird flu.
The deadly H5N1 strain of the virus was found in birds in Romania and Turkey last week. H5N1 has killed more than 60 people in South-East Asia since 2003.
Only one victim is suspected of catching the virus from another person, rather than from a bird - no cases of human-to-human transmission have been confirmed.
Scientists warn the strain could cause a lethal pandemic if it mutates into a form that can be spread from person to person.
UK Foreign Secretary Jack Straw, chair of the EU meeting in Luxembourg, says coordinated action is being taken across the EU, hoping to sway public concerns.
Straw says, "It's on issues like this that the EU comes into its own. Without the resources of the European Union, the coordination and funds that the European Union can bring, Europe would face much greater anxieties about the potential effects of avian flu than are there now."
