Praise be to Allaah. 

Firstly, it is prescribed for a Muslim to initiate the greeting of salaam to his Muslim brother when he is praying, but the one who is praying should not return the salaams whilst praying, except by making a gesture in a manner that will maintain the validity of his prayer, because it was narrated that Ibn ‘Umar (may Allaah be pleased with him) said:

“I asked Bilaal, How did the Messenger of Allaah (peace and blessings of Allaah be upon him) return their salaam when they greeted him whilst he was praying? He said, With a gesture of his hand.”

(Narrated by Ahmad, 6/12; Abu Dawood, 1/569, no. 927; al-Tirmidhi, 2/204, no. 368; al-Bayhaqi, 2/262; also narrated by the five).

 It was also narrated from him that Suhayb (may Allaah be pleased with him) said: “I passed by the Messenger of Allaah (peace and blessings of Allaah be upon him) whilst he was praying. I greeted him with salaam  and he responded with a gesture.” And he said: I am not sure whether he said “a gesture with his fingers”. (Narrated by the five, apart from Ibn Maajah. Al-Tirmidhi said: both hadeeths are saheeh in my view).

 It was reported that Umm Salamah (may Allaah be pleased with her) said: I heard the Prophet (peace and blessings of Allaah be upon him) forbidding us to pray two rak’ahs after ‘Asr, then I saw him praying them when he prayed ‘Asr. She said, he entered and there were some women from Bani Haraam, from among the Ansaar, with me. He started to pray them [these two rak’ahs after ‘Asr], so I sent a young girl to him, and I told her, ‘Stand beside him and say to him, Umm Salamah is saying to you, O Messenger of Allaah, I heard you forbidding us to do these two rak’ahs and now I see you praying them. If he makes a gesture with his hand then leave him and go back.’ So the young girl did that and he made a gesture with his hand, so she left him and went back. When he finished praying, he said: ‘O daughter of Abu Umayyah, you asked about the two rak’ahs after ‘Asr. Some people from Banu ‘Abd al-Qays came to me and kept me from doing the two rak’ahs after Zuhr, and that is what these were.’” (Narrated by al-Bukhaari and Muslim).

 These ahaadeeth indicate that it is prescribed to say salaams to a person whilst he is praying, and that he should respond to the greeting with a gesture, because this is what the Prophet (peace and blessings of Allaah be upon him) approved of initiating the salaam, and he returned the greeting with a gesture only.

 Secondly, it is prescribed for the Muslim to initiate the greeting to one who is engaged in making dhikr or du’aa’, because it was reported that Abu Waaqid al-Laythi (may Allaah be pleased with him) said: “Whilst the Prophet (peace and blessings of Allaah be upon him) was sitting in the mosque and there were some people with him, three people came in. Two of them came to the Messenger of Allaah (peace and blessings of Allaah be upon him) and one went away. When they came up to the Messenger of Allaah (peace and blessings of Allaah be upon him), they greeted him with salaam. One of them found a space in the circle and sat down, and the other sat down behind him. The third one turned and went away. When the Messenger (peace and blessings of Allaah be upon him) had finished (his talk), he said: ‘Shall I tell you about these three people? One of them turned to Allaah so Allaah accepted him; the second felt shy so Allaah will feel shy (to punish him); and the third turned away so Allaah turned away from him.” (Narrated by Maalik in al-Muwatta’, 2/960; Ahmad, 5/219; al-Bukhaari, 1/24, 122; Muslim, 4/1713, no. 2176; al-Tirmidhi, 5/73, no. 2724; Abu Ya’laa, 3/33, no. 1445).

And in al-Saheehayn it is narrated from Abu Hurayrah (may Allaah be pleased with him) that a Bedouin entered the mosque and prayed, but he did not do the rukoo’ and sujood properly. Then he came and greeted the Prophet (peace and blessings of Allaah be upon him) with salaam. The Prophet (peace and blessings of Allaah be upon him) returned his greeting then said, “Go back and pray, for you have not prayed.”

And Allaah is the Source of strength. May Allaah bless our Prophet Muhammad and his family and companions, and grant them peace.