Sorry, Petrus, but UncleLuc is correct. The date is written in the Iranian Solar Hegira calendar, which Iran adopted on 31st March AD 1925, shortly after the Pahlavi dynasty came to power. As far as I know, all Pahlavi coins and medals are dated in this calendar (except for some later ones that used the Achaemenid Calendar). 31st March 1925 was the 4th of Ramadan AH 1343, so while Iran in effect had "year 1343" twice, in AD 1924 and AD 1964, it only had "year 1344" once, in 1965.
Here's the silver version of the exact same medal on Zeno.ru, where the owner has helpfully typed out the Persian text from the reverse. Copy-and-pasting this text into Google Translate gives the following:
On the occasion of the twenty-fifth year of the reign of His Majesty Homayoun Mohammad Reza Pahlavi, the Shah of Iran, September 1344.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis