"Last September we started to inspect Iranian and Syrian planes at random. We have found non-lethal materials, like equipment, medicine and food," Zebari said in an interview published by the Asharq al-Awsat newspaper.
"In all honesty, those planes might be carrying other stuff, but we have neither the deterrent means, nor the air defences and fighter jets to prevent... Arms shipments," he told the pan-Arab daily.
Zebari said he had urged Western governments to take action themselves if they were convinced that Iran was smuggling weapons to its Syrian ally.
Zebari said Western governments were convinced such an air bridge existed and that his response was: "This does not have my consent, and I do not have the means to prevent it."
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He said the Shiite-led government in Baghdad had urged Tehran "not to use relations with (Iraq) to send arms to others."
"We reject and condemn the shipping of arms through our airspace, and we will tell the Iranian side of that officially, but we cannot stop it," Zebari said.
The conflict in Syria has become increasingly sectarian as it has entered its third year, with the mainly Sunni rebels receiving support from the Gulf Arab monarchies, and the Damascus regime getting backing from Shiite Iran.
But he stressed that their involvement in the conflict "does not come under government policy.