In his letter, Taghipour says that banned foreign e-mail providers include Yahoo, Hotmail, Gmail, and MSN.
The communications minister has called on banks to only accept national e-mail addresses from customers when they open accounts.
Taghipour has requested that banks provide access to the Internet for customers to be able to create national e-mail accounts at their premises.
The move appears to be aimed at forcing citizens to join the national e-mail system, which many Iranians have been reluctant to use.
Some Iranian websites have reported that the use of the national e-mail is obligatory for those working for the government and state institutions.
Iranians have complained several times in recent months that access to their Gmail and other foreign e-mail accounts has been disrupted.
These complaints came at a time when the Iranian media reported that the national e-mail system had been also disrupted.
Officials did not provide any explanation for the disruption, which angered many.
Iran's national e-mail system is part of efforts by Tehran to launch its own national Internet, which could further limit Iranians' access to the free flow of information online.
The latest edition of Freedom House's "Freedom of the Press" survey listed Iran in its usual place among the "worst of the worst."
Christopher Walker, vice president for strategy and analysis at Freedom House, told RFE/RL that the country’s government "defines itself by the ferocity of its crackdowns, both on online and traditional media."
-- Golnaz Esfandiari