Sheikh `Atiyyah Saqr, former head of Al-Azhar Fatwa Committee, states in this regard: “Originally, it is reprehensible or Makruh to salute the person (i.e. to say Salamu `Alaykum) to the person who is busy reciting the Qur’an. However, if someone salutes the person who is reciting the Qur’an, then it is obligatory (according to the opinion which is deemed to be the most correct) upon the person addressed to respond, and then resume his reading. It is not sufficient in saluting the person to make a sign as one should respond using the well known Salam words.”
Thus, it has become clear that if someone says “Salamu `Alaykum” to you while you are reciting the Qur’an, it is obligatory upon you (i.e. (according to the preponderant opinion) to have a brief pause, respond to his salutation, and resume your recitation.”