The supplication made between the adhan and the iqamah is not rejected.
Sunan Abi Dawud Book 2, Hadith 131
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I came to the prophet (ﷺ) at Mecca; he was sitting in a tent made of leather. Then Bilal came out and called to prayer. I looked at his mouth following him this side and that side (i.e., right and left). Later at his Messenger of Allah (ﷺ) came out clad in a red suit, i.e, wearing the sheets of the Yemen, of the Qatri design. The version narrated by Musa has the word; “I saw Bilal going towards al-Abtah”.
He then made a call to prayer. When he reached the words “ come to prayer, come to salvation”. He turned his neck right and left, respectively; he did not turn himself (with his whole body). He then entered (his house) and came out with a lancet. The narrator then reported the rest of the tradition.
Sunan Abi Dawud Book 2, Hadith 130 Next Hadith → When you hear the Adhan, you should repeat the same words as the mu’adhdhin pronounces.
Sunan Abi Dawud Book 2, Hadith 132
He then made a call to prayer. When he reached the words “ come to prayer, come to salvation”. He turned his neck right and left, respectively; he did not turn himself (with his whole body). He then entered (his house) and came out with a lancet. The narrator then reported the rest of the tradition.
Sunan Abi Dawud Book 2, Hadith 130 Next Hadith → When you hear the Adhan, you should repeat the same words as the mu’adhdhin pronounces.
Sunan Abi Dawud Book 2, Hadith 132