Responding to the muezzin Azan is better than reading holy Quran
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If a person is reading Qur’aan and the muezzin gives the call to prayer, it is better for him to stop reading and focus on following the muezzin, in obedience to the general meaning of the words of the Prophet (blessings and peace of Allah be upon him): “When you hear the muezzin, say what he says” (narrated by Muslim, 384); and delaying it will mean you miss the right time for doing it, which is the time of the adhaan.
Imam al-Nawawi (may Allah have mercy on him) said:
When he hears the muezzin, he should stop reading and follow the muezzin, repeating the words of the adhaan and iqaamah, then go back to his reading. This is what is agreed upon by our companions. End quote from al-Tibyaan fi Adaab Hamlat al-Qur’aan, 126.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him) was asked: If the muezzin gives the call to prayer whilst a person is reading Qur’aan, is it better for him to repeat after him and say what he says, or should he focus on reading Qur’aan on the grounds that it is better and one should give precedence to that which is better?
He replied: The Sunnah, if one is reading Qur’aan and hears the adhaan, is to respond to the muezzin, following the teaching of the Prophet (blessings and peace of Allah be upon him): “When you hear the muezzin, say what he says, then send blessings upon me, for whoever sends blessings upon me, Allaah will send blessings upon him tenfold. Then ask Allaah to grant me al-waseelah, for it is a station in Paradise which only one of the slaves of Allaah will attain, and I hope that I will be the one. Whoever asks for al-waseelah for me, intercession will be permissible for him.” Narrated by Muslim in his Saheeh from the hadeeth of ‘Abd-Allah ibn ‘Amr ibn al-‘Aas (may Allah be pleased with him).
In al-Saheehayn it is narrated from the hadeeth of Abu Sa‘eed al-Khudri (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “When you hear the muezzin, say what he says.” In Saheeh al-Bukhaari it is narrated from Jaabir ibn ‘Abd-Allah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: Whoever says when he hears the call to prayer, ‘Allaahummah Rabba haadhihi’l-da’wat il-taammah wa’l-salaat il-qaa’imah, aati Muhammadan al-waseelata wa’l-fadeelah, wab’athhu maqaaman mahmoodan alladhi wa’adtahu (O Allaah, Lord of this perfect Call and the Prayer to be offered, grant Muhammad the privilege and also the eminence, and resurrect him to the praised position that You have promised), will be granted my intercession on the Day of Resurrection.” al-Bayhaqi added with a hasan isnaad: “innaka la tukhlif al-mi‘aad (Verily You never break Your promise).” And because answering the muezzin is a Sunnah which will be missed out if he carries on reading, whereas he will not miss out on reading because the times when he can read are plentiful. May Allah help and guide us all.
End quote from Majmoo‘ Fataawa Ibn Baaz, 10/358
And it may be the case that what is less virtuous may become more virtuous in certain cases. For example, reading Qur’aan is one of the best kinds of dhikr and the Qur’aan is the best of dhikr. If a man is reading Qur’aan and hears the muezzin gave the call to prayer, is it better for him to carry on reading or to answer the muezzin? In this case we say: it is best to answer the muezzin, even though Qur’aan is better than dhikr. Dhikr at the appropriate time is better than reading Qur’aan, because reading Qur’aan is not connected to a specific time; whenever you want to you can read it, but responding to the muezzin is connected to hearing the adhaan. End quote from Liqaa’aat al-Baab al-Maftooh.
And Allah knows best.