What does the bereaved say to the one offering condolences on the death of a relative?

There is no specific wording for offering condolences; rather, anything that expresses solace and encourages patience is desirable. It is best to use the phrases that were reported from the Prophet, peace and blessings be upon him. As for the person being condoled, there is nothing specific in the Sunnah (definition) to be said in response to condolences. It is permissible to say: "May Allah reward you with good" or "May Allah answer your supplication." Ibn Qudamah narrated that Imam Ahmad said to someone who offered him condolences: "May Allah answer your supplication, and may He have mercy on us and on you." Sheikh Ibn Uthaymeen was asked about the prescribed supplications for offering condolences, and he said that the best way to offer condolences is: "(Indeed, to Allah belongs what He has taken, and to Him belongs what He has given, and everything with Him has an appointed term. So be patient and seek your reward from Allah)." He also said that the person being condoled should say: "May Allah thank you, and may Allah help us bear up and be patient."