The letter which appeared in Morsi's official Facebook page yesterday went viral on the Muslim Brotherhood websites and other social media platforms.
The letter started with congratulating Muslims on the occasion of the New Hijrah (Islamic) Year - that Muslims celebrates today - and described the country as 'still at the zenith of its revolution and the youth are at the peak of their determination to implement their will'.
"I congratulate you and express delight at the continuation of your revolution against the lame coup and its leaders who seek to subjugate the country to their whims. Yet, they will never succeed. They live in fear of a black fate awaiting them as a punishment for what they have perpetrated of crimes against the great Egyptian people," the letter said.
In the letter, Morsi also said that he is continuing to reject all the attempts to negotiate a compromise at the expense of the revolution and the blood of the martyrs.
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"I would like to stress to all revolutionaries active on the ground as well as their leaders, councils, alliances, symbols, thinkers and students: "No recognition of the coup, No retreat from the revolution, No negotiation or compromise on the blood of the martyrs," the letter said.
"I have not and will not forget the martyred soldiers assassinated by treacherous criminals after the coup turned the whole country into rivers of blood. I believe only the revolution will heal the wounds of our country," the letter added.
The jailed Islamist ex-president, ousted by the army last year, already faces charges over the killing of peaceful protesters, espionage, escaping from prison during the Egyptian Revolution in 2011, and insulting the judiciary.
Egypt has also jailed Al-Jazeera journalists for allegedly aiding Morsi's Muslim Brotherhood.