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Shiavault - a Vault of Shia Islamic Books Muawiya Rasulullah (s) Made Three Dua's, One That Was Rejected We read in Sahih Muslim Book 041, Number 6904: "Thauban reported that Allah's Messenger (may peace be upon him) said: Allah drew the ends of the world near one another for my sake. And I have seen its eastern and western ends.
And the dominion of my Ummah would reach those ends which have been drawn near me and I have been granted the red and the white treasure and I begged my Lord for my Ummah that it should not be destroyed because of famine, nor be dominated by an enemy who is not amongst them to take their lives and destroy them root and branch, and my Lord said: Muhammad, whenever I make a decision, there is none to change it.
Well, I grant you for your Ummah that it would not be destroyed by famine and it would not be dominated by an enemy who would not be amongst it and would take their lives and destroy them root and branch even if all the people from the different parts of the world join hands together (for this purpose), but it would be from amongst them, viz. your Ummah, that some people would kill the others or imprison the others".
Rasulullah (s) was fully aware in his Prophetic capacity of the fitnah that would befall the Ummah after him, and he foretold in clear traditions that Imam 'Ali (as) would face stiff opposition, that he would fight those who opposed his Leadership, the Qasatheen.
Mu'awiya was the Leader of the opposition / Fitnah group, hence even if for arguments sake we were to accept Rasulullah (s) making such a dua, it would have been rejected on account of Mu'awiya's enmity and condemnation by Rasulullah (s) of those that shall fight Imam 'Ali (as).
Rasulullah (s) even prayed for Abu Jahil to be guided Amongst Ahl'ul Sunnah's traditions in praise of Hadhrath Umar, they commonly cite this one that we have taken from Riyadh ul Nadira Volume 2 page 13: "Rasulullah made a dua, O Allah Strengthen Islam by either Umar bin Khattab or Abu Jahil, whoever you prefer more". Here Rasulullah made a du'a for Abu Jahil to be guided to the truth but this never transpired, and his example is very much like Mu'awiya's.
We even learn in Sahih al Bukhari Volume 8, Book 75, Number 406 that Rasulullah (s) made dua for the pagans: At-Tufail bin 'Amr came to Allah's Apostle and said, "O Allah's Apostle!