The military, then led by the now president Abdel Fattah El Sisi, removed Morsi amid mass rallies against his rule.
But hundreds of Muslim Brotherhood members in Turkey took to the streets of Ankara and Istanbul, some of them blaming Egyptian authorities for the death.
Morsi had been sentenced to more than 40 years in prison in separate trials, including for leading an outlawed group, spying for foreign country and terrorism.
He was overthrown by the army in 2013. State TV, citing an unnamed medical source, said he died after suffering a heart attack.
No significant increase in security in central Cairo was noticeable on Tuesday morning. His legacy: the unprecedented consolidation of authoritarian rule by Egypt's current military regime.
Virtually overnight, imperialist politicians in Washington and the European capitals-who had hailed Mursi as Egypt's first "democratically elected" president when they hoped his election would prevent revolutionary struggle by the working class-abandoned Mursi, leaving him to rot in jail. The Muslim Brotherhood, the Islamist organization to which Mursi belonged, issued a statement on its web site yesterday, declaring: "Neither the shock of the news nor the haste in spreading information about the details of his death will change the features of this full-fledged murder".
Mursi's death is likely to increase worldwide pressure on the Egyptian government over its human rights record, especially conditions in prisons. "Sisi is the murderer and there must be a transparent and independent worldwide investigation".
The Egyptian authorities "put him in solitary confinement".
Mursi, 67, fainted in the defendant's cage after speaking at the court hearing and died instantly.
The ex-president's death after six years in jail under the military-backed establishment that ousted him in 2013 stoked anger among his supporters in Egypt and overseas.
Another of Morsi's legal defence team described the moment he received news of his death.
"May Allah have mercy on Dr. Mohamed Mursi, the former President of Egypt, and grant him a place in paradise and forgiveness".
His death is likely to pile global pressure on the Egyptian government over its human rights record, especially conditions in prisons where thousands of Islamists and secular activists are held.
"The Egyptian people won't let this crime pass lightly even after a while", he added.
Sissi has since closely aligned his country with Saudi Arabia, whose royal family is deeply critical of the Muslim Brotherhood.
In a new ethical low for Human Rights Watch, Sarah Leah Whitson, Director of the Middle East and North Africa division of HRW, published a number of tweets on her account regarding the circumstances of the passing of the deposed president, Mohamed Morsi.
After his arrest, Morsi gave angry speeches in court and continuously insisted he remained Egypt's legitimate president.