The decision comes as the country prepares for a second round of voting on a draft constitution. Opponents of President Mohamed Morsi, who appointed Abdallah, have said they will continue to oppose the constitution if it passes.
Abdallah agreed to quit Monday as lower-level prosecutors surrounded his office, accusing Morsi and his top aides of trying to use the judicial system for political purposes, The New York Times reported.
Morsi's party called the protesters "street thugs" and accused them of carrying weapons. In a statement, the party said Egypt would be "governed by the law of the jungle" if top-level officials could be forced out by employee demonstrations.
Large protests are planned before Saturday's voting.
Opposition marches by groups including the Revolutionary Socialists, the Strong Egypt Party, the 6 April Youth Movement and the Socialist Popular Alliance are scheduled to lead up to the second round of the referendum, Ahram Online reported Thursday.
The first round of the referendum illustrated the deep divide within post-revolutionary Egypt, with the measure being approved by 54 percent of the voting population and opposed by 44 percent.
Some opposition members said the referendum should not pass if the votes are this close come Saturday.
"No country in the world would accept a constitution pass with only 50 percent of the population in agreement," said George Ishak, member of the National Salvation Front and founding member of the Dostor (Constitution) Party.
"In France, when only 54 percent of the population agreed on the constitution it remained in dispute until 85 percent consented," he added.
Bas el-Adel, president and founder of the liberal Nile Party, said he would continue to fight against the proposed constitution, even if it passes Saturday.
"In 1913, we had a similar constitution that took five years to bring down. We will fight until the same occurs today!" he said.
Egypt witnessed several days of deadly demonstrations ahead of last weekend's vote. Some political groups and movements have expressed frustration with the direction of a country now led by the Freedom and Justice Party, a party formed by the Islamist Muslim Brotherhood, which supports Morsi.