Shaykh Muhammad Naasirud-Deen Al-Albaanee
Source: Akhlaaqul-Islaam, Tape #1 of 9,
Translated exclusively for www.bakkah.net
In our last lesson we discussed the hadeeth of 'Aa'ishah (may Allaah be pleased with her) who heard the Jews greeting the Messenger of Allaah saying, 'As-saamu 'alaykum' ('Death to you'). While the Prophet (sallallaahu 'alayhe wa sallam) simply returned it saying, 'wa 'alaykum' (and to you also), 'Aa'ishah added to it, saying, "and to you also, and the Curse of Allaah and His Anger." 
I also mentioned that the Prophet (sallallaahu 'alayhe wa sallam) prohibited us from initiating the greeting with them. So if the affair is like this, then this shows us that the Muslim is required to interact with the non-Muslim under Islaamic rule within the constraints of the Sharee'ah and not out of one's emotions of love or anger.
So if a man from among the Jews and Christians greets us with the Islaamic greeting, saying, "As-salaamu 'alaykum," some people understand from this hadeeth that we return the greeting with 'wa 'alaykum' and nothing more. So is this correct or are there other details to consider?
If we look to another hadeeth of the Prophet (sallallaahu 'alayhe wa sallam) found in Saheeh Muslim:
"Verily if the Jews greet you, and one of them says,
As for when their greeting is clear and explicit, as is the case with some of them who interact with the Muslims nicely, they clearly pronounce the greeting saying, 'As-salaamu 'alaykum,' should we say, 'wa 'alaykum' or 'wa 'alaykumus-salaam'? Let us look to the Qur'aanic text :