All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
All Muslim scholars are agreed that the words of Iqamah are the same as those of the Athaan except the words 'Qad Qamatis Salah' (twice) which are added in Iqamah. Also, they are agreed that the sequence of the words in Iqamah is also the same as in the Athaan. However, they disagreed as far as repeating the words of Iqamah is concerned. The details are as following:
Saying the first Takbir “Allahu Akbar” twice according to three schools of jurisprudence and four times according to the Hanafi School of jurisprudence. The words “Ashhadu Anllaa Ilaaha Illa Allah, Wa Ashhadu Anna Muhammadan Rasoolullah”, “Hayyi ‘Ala as-Salah”, “Hayyi ‘Alal Falaah” are pronounced once according to the three schools of jurisprudence while Hanafi School of jurisprudence is of the opinion that they are pronounced twice.
The expression ‘Qad qamatis Salah’ is repeated twice according to the three schools of jurisprudence while the Maaliki School of jurisprudence is of the opinion that it should be pronounced only once.
The last Takbeer “Allahu Akbar” is repeated twice and “La Ilaaha Illa Allah” once with no disagreement among the Four Schools of jurisprudence. Among the Ahadeeth that describe the characteristic of the Athaan is the Hadeeth of Ibn ‘Umar who said: “The words of the Athaan were repeated twice during the era of the Prophet of Allah and the words of Iqamah were said once, with no repetition except for the expression: “Qad qamatis Salah” which was repeated twice. [Ahmad and an-Nasaa'i]
The other scholars also have some proofs and pieces of evidence for their claims.
Finally, we draw the attention of our brothers to the fact that the difference of opinion in such matters should not lead to hatred or dispute.
The Imam of the mosque could have retrained from repeating the Iqamah. But anyway, those matters that are subject to Ijtihad should not be a reason for dispute among the Muslim Ummah.
For more benefit, please refer to Fataawa 84974, 83388, and 84204.
Allah knows best.