His resignation had not yet been accepted by the Supreme Judiciary Council, Ahram Online reported.
Abdallah's decision to step down came under mounting pressure from judges and prosecutors, including hundreds who protested at his office earlier in the day, the Egyptian news website said.
They talked to an aide but were denied the opportunity to talk with Abdallah directly. Security forces kept a group of protesters from entering his office.
Abdallah's deputy, Adel El-Said, later presented Abdallah's handwritten resignation to the protesters, Ahram Online said.
The judges and prosecutors were angered by the president's decision to replace Mubarak-era Prosecutor General Abdel-Meguid Mahmoud with Abdallah, the website said.
Morsi appointed Abdallah after issuing his constitutional declaration, which was aimed at exempting his decisions from judicial challenge.
Mahmoud has since been appointed as head of Egypt's Court of Appeal.
After his appointment, Abdallah announced he would retry Mubarak-era Interior Minister Habib al-Adly and other former Mubarak officials on charges of killing protesters, al-Masry al-Youm reported at the time.
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