I believe that when our prophet had a conversation with Christian people, they refused to accept him as a prophet. So he took the notes from their Holy books & proved to them that He as the last messenger & they should accept him as a last messenger & obey his words. When they refused to accept that, Allah sent the verse 3:61 which speaks about the “MUBAHALA”
Now the question is
1. Whether the “MUBAHALA” should be done only between the people (who are do monotheist) & Muslims. (Or) It can be done between two Muslims.
2. According to my knowledge, after that there were so many disputes in the Muslim history & no one invited for the “MUBAHALA”. So inform me, whether that particular verse was abrogated by Allah (like Qibla) by any other verse. If yes, Please give the background Hadith & the verse also. Kindly ref the verse No. 3:64.
I kindly request you to provide the answers with Quran, Hadith book & nos.
As this is the first time to visit this site, I am not aware of your answer systems. So I kindly request you to send the reply to my email ID.
Thanking You.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

The reason why the verse of Mubahalah challenge, no 61 of Surah Aali-Imran was revealed, according to the books of Tafseer (interpretation of the Qur'an), is that the Christians of Najran came to the Prophet (Sallallahu Alaihi wa Sallam) and started to argue with him about Isa (Jesus) and this verse was not abrogated.

The evidence is that many companions called to the Mubahalah (to pray and invoke sincerely the curse of Allah upon those who lie). Among them is Abdullah Ibn Mas'ood, (may Allah be pleased with him), who called to prove that the waiting period (Iddah) of a pregnant woman ends when she gives birth to the baby,  not three months as is normal.  Among them also is Ibn Abbas, (may Allah be pleased with him), who called to Mubahalah in the issue related to the reduction of inheritance's shares (when it is not possible for every heir to take his original share).

As regards whether this is permissible between Muslims, the answer is that it is permissible; the evidence is that the companions did so, as we already mentioned.

However, it is more appropriate for a Muslim not to invoke the curse of Allah upon a Muslim except after establishing the evidence against him, trying to eradicate the misconception, advising and warning him.

Allah knows best.