Hamas says Yousef Abu Zuhri died from internal bleeding. He was the brother of spokesman Sami Abu Zuhri.
On Tuesday, another spokesman, Fawzi Barhoum, urged Egypt to investigate.
An Egyptian prison official says Abu Zuhri died of heart and kidney failure due to pre-existing conditions.
A security official in Cairo said the man was not tortured. Both spoke on the condition of anonymity because they were not authorized to speak to the press.
International human rights groups say torture is systematic in Egyptian jails.
Abu Zuhri was arrested in April for entering Egypt illegally.