How should we return the greeting of salaam from a non-Muslim?

Praise be to Allaah.

It is not permissible – firstly – to initiate the greeting of
salaam to a non-Muslim. The Prophet
(peace and blessings of Allaah be upon him) said:
“Do not initiate the greeting of salaam to a Jew or a Christian…” (Narrated
by Muslim, 2167).

If one of them says “As-Saam ‘alaykum” –
meaning, may death be upon you – or it is not clear whether they have said
“salaam”, then we should respond by saying “Wa ‘alaykum”
(and upon you).

It was reported that Ibn ‘Umar (may Allaah be pleased with him)
said: the Messenger of Allaah
(peace and blessings of Allaah be upon him) said:
“When the Jews greet you, they say ‘Al-saam ‘alaykum (may death be
upon you),’ so respond by saying ‘‘alayk (and also upon
you).’” (Narrated by al-Bukhaari, 5902; Muslim, 2461).

If a non-Muslim greets us with the correct shar’i greeting (i.e.,
says ‘Al-salaamu ‘alaykum’ clearly), the scholars differed as to
whether we have to return the greeting. The majority of scholars said that we do have to
return the greeting, and this is the correct view.

Ibn al-Qayyim (may Allaah have mercy on him) said: they differed as to
whether it is obligatory to return the greeting. The majority said that it is obligatory
and this is the correct view. A group of scholars said that it is not obligatory to return
their greeting just as it is not obligatory to return the greeting of those who follow
bid’ah. But the correct view is the first one. The difference is that we are
commanded to forsake the followers of bid’ah by way of rebuke and to warn
others about them, which is not the case with the Ahl al-Dhimmah (Jews and
Christians).

(Zaad al-Ma’aad, 2/425, 426)

The Muslim who is returning the greeting should respond in the manner
prescribed by sharee’ah, giving a similar or better greeting, because of the general
meaning of the Aayah (interpretation of the meaning):

“When you are greeted with a greeting, greet in return with
what is better than it, or (at least) return it equally.” [al-Nisa’ 4:86]

Ibn al-Qayyim (may Allaah have mercy on him) said: if the person is
certain that the Dhimmi (Jew or Christian) is clearly saying ‘al-salaamu
‘alaykum’ to him, and he has no doubts about that, should he say ‘wa
‘alayka al-salaam’ or shorten it to ‘wa ‘alayk’? What
is indicated by the evidence and principles of sharee’ah is that he should say ‘wa
‘alayka al-salaam’, because this is more just, and Allaah commands us to be
just and to treat others well… this does not contradict any of the ahaadeeth on this
topic at all, because the Prophet
(peace and blessings of Allaah be upon him) commanded
us to shorten the greeting to ‘wa ‘alayk’ because of the
reason mentioned above, which is that they deliberately used to say ‘al-saam
‘alaykum’ instead of ‘al-salaam ‘alaykum’, as
indicated in the hadeeth narrated by ‘Aa’ishah (may Allaah be pleased with her).
He said, “Do you not see that I say ‘wa ‘alaykum’ when they say
‘al-saam ‘alaykum’?” Then he said, “If the People of the
Book greet you with salaam, say, ‘Wa ‘alaykum.’”

Allaah says (interpretation of the meaning):

“… and when they come to you, they greet you with a
greeting wherewith Allaah greets you not, and say within themselves, ‘Why would
Allâh punish us not for what we say?’…” [al-Mujaadilah 58:8]

If this reason is not there, and the Jew or Christian says, ‘Salaam
‘alaykum wa rahmat-Allaah,’ then it is only fair to respond in kind.

(Ahkaam Ahl al-Dhimmah, 1/425, 426)

The hadeeth of ‘Aa’ishah was narrated by al-Bukhaari (5901)
and Muslim (2165)

See also: Majmoo’ Fataawa Ibn ‘Uthaymeen, 2/97

And Allaah knows best.