ANKARA, Turkey — International agencies warned against panic but cautioned Wednesday that Turkey’s neighbors may be unable to keep out the bird flu that has infected at least 15 people across the country in the last week.

Nations bordering Turkey continued to step up preventive measures, disinfecting cars at border crossings, handing out leaflets and blocking people carrying birds. But health officials said the measures may prove insufficient.

‘‘The virus may be spreading despite the control measures already taken,’’ said Juan Lubroth, senior animal health officer at the U.N. Food and Agriculture Organization.

Preliminary tests in the last week indicate that 15 people in Turkey have been infected with the deadly H5N1 strain — the largest number of cases in a single week since late 2003, when the virus began sweeping Asia. Three children have died, but only two of those cases were confirmed to have tested positive for bird flu.

Greece was sending 500 veterinary staff to border areas and spraying cars and trucks from Turkey with disinfectant. Bulgaria told its citizens to avoid contact with birds. Syria stepped up checks on entering Turks. Georgian television broadcast images of panicked villagers in a border region killing chickens, geese and ducks en masse.

‘‘The worst situation is a panic situation. There is no reason to panic,’’ Dr. Marc Danzon, WHO regional director for Europe, told reporters at a joint news conference with Turkey’s health minister.

Greece also is gathering enough antiviral drugs to supply 5 percent of the country’s 11 million people.

‘‘Whatever is humanly possible is being done. The development of the disease in Turkey is not good. ... We must not panic and we must not relax,’’ Greek Health Minister Nikitas Kaklamanis said after an emergency ministers’ meeting on bird flu.

Danzon said there were no signs that the deadly strain was being transmitted person to person in Turkey, where all of the cases appeared to have involved people who touched or played with infected birds.

Health experts have been watching closely for indications that H5N1 is mutating into a potent form passed between people, which could cause a pandemic capable of killing millions.

Turkey’s government, anxious to demonstrate to its citizens and the European Union that it was taking decisive action, ordered more than 300,000 fowl destroyed as a precaution. Authorities also distributed leaflets in eastern regions most affected by the outbreak, cautioning people not to touch fowl, while TV spots urged people to wash their hands after contact with poultry.