The mallard was found in Szentendre, a town north of Budapest, while the gull was found in Szazhalombatta, 30 kilometers south of the capital.
One of the dead swans reported on Wednesday was found 100 kilometers south of Budapest in Dunaszentbenedek, while the other in Nagybaracska.
Hungarian experts feel that the deadly H5N1 virus would mutate in to a form that can infect humans.
The Hungarian government is still waiting to get the confirmation from the Weybridge laboratory in the United Kingdom.
The government spokesman Andras Batiz said that the H5N1 virus has not been detected in domestic poultry in Hungary.