Wa`alaykum As-Salaamu Warahmatullahi Wabarakatuh.
In The Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Thank you very much for your question and for your interest in Islam’s teachings.
In his response to the question, Dr. Muzammil Siddiqi, former president of the Islamic Society of North America (ISNA), states the following:
There is a great reward in making du`aa’ after the obligatory prayers. It is reported in a Hadith that the Prophet, peace and blessings be upon him, was asked “Which Du`a is more heard (by Allah)?” The Prophet (peace and blessings be upon him) says, “The du`aa’ during the last part of the night and after the obligatory prayers.” (At-Tirmidhi)
Imam Al-Bukhari and Imam Muslim have mentioned many Adhkar and supplications of the Prophet, peace and blessings be upon him, that he used to make after the obligatory prayers. This means that the Prophet (peace and blessings be upon him) used to make these supplications audibly or (jaran in Arabic).
It stands to reason that many of the Prophet’s Companions, may Allah be pleased with them all, have mentioned such Adhkar and supplications that they heard from the Prophet, peace and blessings be upon him. I am sure the Companions used to sit and listen to those adhkar and supplications from the Prophet, peace and blessings be upon him. It is a good habit to make dhikr and du`aa’ after the obligatory prayers.
It is, however, not mentioned that the Prophet, peace and blessings be upon him, used to have a collective dhikr or du`aa’ after each prayer. He never asked his Companions to sit with him after the prayer to make du`aa’ with him.
Thus, we can say that it is permissible for the Imam to make du`aa’ audibly or quietly after the obligatory salah. However, it is up to the people to stay or not to stay. Those who want can stay and make the du`aa’ with the Imam or by themselves and those who want to leave without making du`aa’ or to begin their Sunnah prayers, then can do so. Muslims should not make it an issue of division or dissension among them.
It is not right to insist on all people to stay until the du`aa’ is finished and it is also not right to criticize those who make du`aa’ with their Imam after the salah.
For the sake of those who want to perform Sunnah (supererogatory prayers) immediately after the prayer, it is better that the Imam make a short or quietdu`aa’ after Zuhr, Maghrib and `Isha’ prayers, but he may make an audible and longer du`aa’ after Fajr and ‘Asr prayers. And if the Imam sometimes leaves without making du`aa’ that is also permissible.
Allah Almighty knows best.