Morsi, Egypt's first democratically elected president who was arrested after being overthrown in a military coup led by el-Sisi in 2013, died on Monday after collapsing inside his soundproof glass cage while on trial in a Cairo courtroom on espionage charges.
In a Twitter post on Thursday, Morsi's son, Abdullah, named a number of officials whom he called "partners" of el-Sisi "in killing the martyr president".
He particularly accused incumbent and former interior ministers Mahmoud Tawfiq and Magdy Abdel Ghaffar, respectively.
He also named judges Shirin Fahmy, Shaaban al-Shami and Ahmed Sabry, as well as Attorney General Nabil Sadek and Abbas Kamel, the head of the intelligence service.
Egyptian authorities have yet to comment on the claims by Morsi's son.
At the time of his death, Morsi - a leading member of Egypt's Muslim Brotherhood who won the country's presidential election in 2012 - faced a host of legal charges, which he, along with various human rights groups and independent observers, said were politically motivated.
Morsi's death was mourned by many people around the world, including in Turkey, where mosques held special prayers on Tuesday, while leaders in Malaysia and Qatar were among those offering tributes.
However, the reaction has been largely muted in many capitals.
"Mohamed Morsi flailed on the courtroom floor for 20 minutes and the authorities did not help him. This is why I say Morsi did not die, he was murdered," Erdogan told supporters on Wednesday at an election rally in Istanbul.
"We, as Turkey, will follow this issue and do everything possible for Egypt to be tried in international courts for Morsi's death," he said, calling on the Organisation of Islamic Cooperation to take action towards this end.
Since Morsi's removal, relations between Ankara and Cairo have plummeted with acrimonious exchanges.
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