Aref said U.S. demands for Tehran to drop uranium enrichment entirely were "a joke".
The foreign minister said the damage to the nuclear facilities in Iran after U.S. and Israeli strikes was serious and was being evaluated further.
The snapback mechanism can be used to restore U.N. sanctions before the U.N. Security Council resolution enshrining the deal expires on October 18.
The Israeli and U.S. strikes targeted a nuclear programme which Western countries have long said was aimed at building an atomic weapon.