The Egyptian prosecutor, cited by Reuters, said Morsi collapsed while sitting in a defendants' cage in the courtroom shortly after speaking and was pronounced dead in hospital at 4:50 p.m. local time (1450 GMT). Initial investigation showed no signs of recent injury on his body.
According to local media reports, during a trial session for espionage held in Cairo, Morsi suffered a heart attack.
Amnesty International on Monday urged Cairo authorities to investigate the death of the former Egyptian president.
"We call on Egyptian authorities to conduct an impartial, thorough and transparent investigation into the circumstances of Mursi's death, including his solitary confinement and isolation from the outside world", Amnesty tweeted in Arabic, cited by Reuters.
The watchdog also called for a probe into Morsi's medical treatment.
Morsi won Egypt's presidential election in 2012, becoming the first democratically-elected president in the country's history. The following year, he was ousted by the Egyptian military after large anti-government protests. Hundreds of Egyptians were reportedly killed as a result of riots and clashes following the protests.
Morsi is one of 25 representatives of the Muslim Brotherhood movement who had been charged in the ongoing trial.
Born in 1951, Morsi graduated from Cairo University in 1978 with a masters degree in metallurgical engineering. He then moved to the United States, and received a Ph.D. in materials science from the University of Southern California in 1982. In 1985, Morsi returned to Egypt to teach engineering at Zagazig University. He began his political career by successfully running for membership in the Egyptian parliament in 2000.
An uprising on 25 January 2011 unseated Egypt’s longtime ruler Hosni Mubarak. Morsi, who was nominated by the Muslim Brotherhood, won the presidential election in June 2012.
After Morsi was removed from power, five criminal cases were opened against him, including those in connection with clashes near the presidential palace between his supporters and opposition in December 2012; espionage in favor of Qatar and the Hamas movement; his escape from prison during the 2011 mass riots, and allegations that Morsi insulted judges. In 2015, a criminal court in Cairo sentenced Morsi to death for orchestrating a 2011 prison break and leaking state secrets.
*The Muslim Brotherhood is a terrorist group banned in Russia and many other countries.