Can Iran Retake European Pistachio Market From US?

As the biggest pistachio producers in the world, Iran and the US have always had close rivalry in the production and export of the expensive nut. 
According to Iran Pistachio Association, the two countries account for 85% of world production of pistachios (dry in-shell basis).
With the trade war heating up between the US and Europe, it could affect the Iranian economy in some ways. Iranian pistachios were banned from EU markets in 1996 due to high aflatoxin contamination levels. Since then, Americans managed to dominate most of Europe’s pistachio markets.  
However, according to Mohsen Jalalpour, the former head of Iran Chamber of Commerce, Industries, Mines and Agriculture, things seem to be changing in Iran's favor.