The consulates of Belgium, Canada, Germany, France and the United States -- all countries involved in the international coalition against Islamic State (IS) jihadists -- had reported receiving the yellow powder on Friday.
The Hungarian consulate informed the authorities today that it had also received the powder and experts from Turkey's disaster management agency AFAD were sent to the scene, the Istanbul authorities said in a statement.
The statement said it appeared the powder sent to the Hungarian consulate was likely to have been sent in the same batch as the others, given that the consulate had been closed for the last two working days.
The health ministry said today that tests on samples of the powder collected Friday had showed no evidence of lethal viruses or substances including anthrax, plague, ricin, tularemia or other biological warfare agents.
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However it said that tests were continuing throughout the day and final results would be announced later today.
Hungary announced in August it would send ammunition to Iraq to help the Iraqi authorities fight against the IS jihadists, who have seized large parts of the country.
The scare in Istanbul came amid mounting concerns about the growing national security threat to Turkey and Western states posed by the jihadists, who are trying to seize the town of Kobane close to Turkey's border with Syria.