Is it permissible to delay returning the salam when occupied with supplication or reciting the Qur'an?

The questioner:
May Allah reward you, Honorable Shaykh. This questioner says: It is established that the Prophet (peace and blessings be upon him) was urinating when a man greeted him, so he did not return the greeting. Does this apply by analogy if a person is in a state of supplication or in a gathering of knowledge, and someone greets him, so that he does not return the greeting until he is finished?

The Shaykh:
Yes, yes. If someone greets you and you are occupied speaking with someone, or reciting the Qur'an, or in dhikr (remembrance of Allah), then you delay the response until you are done, and you let him know by informing him so that he does not find fault with you. Yes.

The presenter:
May Allah reward you.

The Shaykh:
It is prescribed for the one being greeted to do what is prescribed, which is to return the greeting, but if that happens, you delay the response. Yes.