First of all, we’d like to state that there are a number of hadiths that confirm that the Prophet (peace and blessings be upon him) made du`a’ after Salah. For example, Sa`d Ibn Abi Waqqas (may Allah be pleased with him) used to recommend these five (statements) and say that the Prophet (peace and blessings be upon him) said so (and they are): “O Allah! I seek refuge in You from miserliness, and I seek refuge in You from cowardice, and I seek refuge in You from being brought back to geriatric old age, and I seek refuge in You from the afflictions of the world, and I seek refuge with You from the punishment of the grave.” (Al-Bukhari, Sahih, vol. 8, hadith no. 381) It was also reported that after performing obligatory prayers, the Prophet (peace and blessings be upon him) used to read the Verse of the Throne (Al-Baqarah: 255) and then utter certain statements which, if one were to utter or observe them at the end of every obligatory Prayer, one would not be dismayed. They are: glorifying Allah thirty-three times, praising Allah thirty-three times and extolling His greatness thirty-three times.

As for the way of making supplication after congregation Prayer, it is up to the people to stay or not to stay and to say the supplications audibly or quietly.

Dr. Muzammil H. Siddiqi, President of the Fiqh Council of North America, states that: “There is a great reward in making Du`a 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`a during the last part of the night and after the obligatory prayers.” (Reported by 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 used to make these supplications audibly or (bil-jahr).
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`a 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`a after each prayer. He never asked his Companions to sit with him after the prayer to make Du`a with him.
Thus, we can say that it is permissible for the Imam to make Du`a 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`a with the Imam or by themselves and those who want to leave without making Du`a 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`a is finished and it is also not right to criticize those who make Du`a 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 quiet Du`a after Zuhr, Maghrib and `Isha prayers, but he may make an audible and longer Du`a after Fajr and ‘Asr prayers. And if the Imam sometimes leaves without making Du`a that is also permissible.”