Over the past month the Centre for Poultry Farming of the National Veterinary Institute has received 2,270 samples for analysis and is yet to test 670 of them.
All tests other than those performed on swans from two fish ponds have returned negative results for the avian influenza virus, the ministry said in a statement.
A dead swan, marked 10JJ and ringed in Hungary, was found to be positive to bird flu. The Centre for Poultry Farming proved the presence of both the H5 and N1 genes in the swan, meaning that the bird was infected with the highly pathogenic H5N1 virus.
The Hungarian veterinary authority has been notified of the finding.