Is it legislated to say "peace be upon you" (As-salamu alaykum) upon entering the mosque when people are engaged in dhikr (remembrance of Allah) or recitation before the iqamah (call to prayer), or is it more preferable to omit it?

Scholars have differed regarding the act of greeting a person reciting the Quran with salam. Al-Wahidi was of the opinion that it is preferable not to greet him, and if one does, it suffices for him to respond with a gesture. If he responds verbally, he should resume with isti'adha (seeking refuge with Allah) and then his recitation.

As for Al-Nawawi, he held that the apparent ruling is the permissibility of greeting him with salam and the obligation to respond.

Regarding one who is engrossed in du'a (supplication), it is possible that his ruling is similar to that of the reciter. However, the more evident view is that it is disliked to greet him with salam due to the difficulty it might cause him.