"Today, respecting consumers' rights is a basic principle which Apple has not followed," Information and Communication Technology Minister Mohammad Javad Azari Jahromi tweeted, promising to "legally pursue" the case.
"IT should be used for making human life better and comfortable not a tool for discrimination between countries," he wrote.
The hashtag #StopRemovingIranianApps has been trending on Iranian social media in the past few days, after Apple removed at least 10 of the country's most popular apps from its online store.
"We are unable to include your app on the App Store," a message sent to some of those companies reportedly said.
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"Under the US sanctions regulations, the App Store cannot host, distribute, or do business with apps or developers connected to certain US embargoed countries."
The US lifted some sanctions on Iran, particularly in the aviation sector, under a 2015 nuclear deal that saw Tehran limit its atomic programme.
But American individuals and companies are still barred from doing any business with Iranians because of much older and non-nuclear related sanctions on the Islamic republic.
Some Iranian apps in the same category of the removed ones are still available on the app store.
Iran's youthful and well-connected population own some 40 million smart phones, six million of them iPhones, the government-owned Iran Daily newspaper reported.
"Apple has not provided any clear answers to our messages," the daily on Saturday quoted Mehdi Taghizadeh, vice chairman at Delion, as saying.
More than 4,500 Iranian netizens have signed an online petition urging Apple chief executive Tim Cook "to recognise our rights as Apple customers".
"Technology is best when it brings people together. We shouldn't limit or keep others from using and developing it!" tweeted Ferial Govashiri, who used to work as a personal assistant to former US president Barack Obama but is now at Netflix.
Owners of devices that run on Android can still download Iranian apps from the online store for Google, also an American company, but they are still unable to use paid apps in the country.