All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The Sunnah for a Muslim when greeting with Salaam is to say ‘‘As-Salaamu ‘Alaykum…’’, this is the greeting of Muslims and one should abide by this form of greeting in the same manner as it is reported in the Sunnah.
As regards saying ‘Salaam’ only, then this is not among the guidance of the Prophet and his companions but if the speaker intends by it to greet and supplicate at the same time for the addressee, as it is intended by the greeting of Salaam in principle, then this is permissible. Indeed, Allaah reported to us the story of His Angels [Quran 11:69] when they came to Ebraaheem (Abraham) in the form of guests and said to him, “Salaam” (Peace), and he replied to them in the same manner “Salaam” (Peace).
Therefore, if a person is greeted by a Muslim with this term, he is obliged to reply the greeting with the same term ‘Salaam’ or with a better greeting.
As regards responding with the term ‘wa alaykum’, then this is not answering the greeting with its equal, rather, a person should avoid responding with such a term because it is the term by which we respond to the non-Muslims when they greet us with Salaam.
For more benefit, please refer to Fatwa 83602.
Allaah Knows best.