Du'a between the Adhaan and Iqaamah in not Rejected
"Du'a between the Adhaan and Iqaamah in not rejected."
"A lot of people neglect making Du'a between the Adhaan and Iqaamah and busy themselves with reciting the Qur'an. Reciting the Qur'an, no doubt is a noble action but reciting the Qur'an has another time. You (should) busy yourself with Du'a and Dhikr which is more virtuous during this time. This is because the Du'a which is restricted (being made) in its appointed time is more virtuous than the unrestricted Du'a (which could be made at any time).
The recitation of the Qur'an is unrestricted in all times. This time (between the Adhaan and Iqaamah) is specific for Du'a so you busying yourself with Du'a, Dhikr and seeking forgiveness is more virtuous than reciting the Qur'an at this time. It is befitting that it is understood."