Egyptian authorities are under pressure after former President Mohammed Morsi collapsed in court and died on Monday.
Morsi, who was 67, had been in custody since his removal from office in 2013.
Amnesty International has called for “an impartial, thorough and transparent investigation” into his death, the authorities say from a heart attack.
His family and activists had raised concerns about his health and the conditions in which he was held, much of the time in solitary confinement.
Reports say he has been buried in Cairo.
A top figure in the now-banned Islamist movement, the Muslim Brotherhood, Morsi became the country’s first democratically elected leader in 2012.
He was ousted and detained in a military coup a year later following mass protests against his rule.
Abdul Fattah al-Sisi, then army chief, has been in power since 2014.
After Morsi’s removal, the authorities launched a crackdown on his supporters and other dissent, leading to tens of thousands of arrests.
The Muslim Brotherhood and Turkish President Tayyip Erdogan are among those who have blamed the Egyptian leadership for Morsi’s death.
Morsi was appearing in Cairo on Monday on charges of espionage related to suspected contacts with the Palestinian Islamist group Hamas.
Officials say he had asked to address the jury, and spoke for about five minutes from a soundproof glass cage where he was being held with other defendants.
Minutes later, he apparently fainted during a break in proceedings.
He was transferred to a hospital where he was pronounced dead,” a statement by Egypt’s public prosecutor said.
Officials said a forensic report had been ordered into his death, and insisted no new, visible injuries were found on his body.
State television had earlier described the cause of death as a heart attack.
Morsi was already facing decades in jail after being sentenced in three other trials. He had previously been given a death sentence, but that sentence was later overturned.
Sarah Leah Whitson, executive director of Human Rights Watch’s Middle East and North Africa division tweeted that his death was “terrible but entirely predictable”.
“Former President Morsi’s death followed years of government mistreatment, prolonged solitary confinement, inadequate medical care, and deprivation of family visits and access to lawyers,” Ms Whitston said in a later statement. The group called on the UN to start an investigation into what it described as “ongoing gross violations of human rights in Egypt, including widespread ill-treatment in prisons”.
Amnesty International also called for an impartial inquiry.
The rights group say Morsi was only allowed three family visits in almost six years of solitary confinement, and was denied access to his lawyers or a doctor.
The Muslim Brotherhood’s political arm, the Freedom and Justice party, described Morsi’s death as an “assassination”.
Turkey’s President Recep Tayyip Erdogan, who was a close ally of Morsi, blamed Egypt’s “tyrants” for his death and described him as a martyr.
The Emir of Qatar, Sheikh Tamim bin Hamad Al Thani, another ally of the late leader, expressed his “deep sorrow” at the death.
British MP Crispin Blunt, who led a panel of politicians who warned in 2018 about the conditions of Morsi’s confinement, has called for a “reputable independent international investigation”.
Born in the village of El-Adwah in 1951, Morsi studied Engineering at Cairo University in the 1970s before moving to the US to complete a PhD.
He was chosen as the Muslim Brotherhood’s presidential candidate for the 2012 election after the movement’s preferred choice was forced to pull out.
During his turbulent year in office, Morsi was accused of mounting an Islamist coup and mishandling the economy.
Public opposition to his government grew and millions of anti-government protesters took to the streets across Egypt to mark the first anniversary of the day he took office, on 30 June 2013.
Three days later, the army suspended the constitution, announced an interim government ahead of new elections and detained Morsi, who denounced the move as a coup.
Then army chief Mr. al-Sisi was elected president in 2014 and re-elected last year in polls rights groups called “farcical”.
Hundreds of people have been killed and tens of thousands of others detained in the subsequent crackdown.