Hamid Aboutalebi was a member of a Muslim student group that stormed the US Embassy in Tehran in 1979 and held 52 Americans hostage for 444 days.
State Department deputy spokeswoman Marie Harf is not saying whether the US would refuse to grant a visa to the envoy.
The UN headquarters are in New York, and because the US is the host nation for the UN, Harf says that the US generally is obligated to admit the chosen representatives of UN member states.