In a letter to UN Secretary-General Kofi Annan and quoted by the IRNA news agency, Pourmohamadi said the move contravenes the United States' international obligations as the host country of the UN and violates Iran's rights.
The letter was delivered to the UN on September 14.
Pourmohamadi had applied for a U.S. visa to attend this week's UN meeting on migration.
There has been no reaction from U.S. officials.
U.S. officials appeared to relax their approach earlier in September when they issued a visa that allowed Iranian ex-President Mohammad Khatami to travel to Chicago and Washington for appearances unrelated to UN business.
The United States cut off normal diplomatic ties with Tehran after Iranian students stormed the U.S. Embassy and took U.S. officials hostage in 1979 following the Islamic revolution.
Relations have been further strained by the Bush administration's inclusion of Iran in what it described as the "axis of evil," along with international fears that Tehran is seeking to develop nuclear weapons and Iran's support for the group Hizballah, which Washington has labeled an international terrorist organization.