"There have indeed been requests and they were rejected," Austrian Colonel Michael Bauer told AFP.
Bauer added that the same applies every time a request to fly into Austrian airspace “involves a country in war.”
Austria has been neutral since 1955.
US President Donald Trump has previously criticized NATO countries France and Spain for denying US military planes en route to the Middle East.
Switzerland also made a similar decision in March, citing its neutrality.
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