Reference: Sharh ‘Umdatil-Fiqh – Tape No.8, Question No.26
Question: Whilst the mu.adhdhin calls the iqaamah, should I repeat what he is saying?
Response: Yes, because the iqaamah is a call to prayer, and is [also] referred to as adhaan. The Prophet ﷺ said:
…meaning a voluntary prayer, and what is intended by «the two adhaans» is the adhaan [itself] and the iqaamah.
So, yes you should repeat the wording of the iqaamah along with the mu.adhdhin, because doing so entails reward.