Tamarud, the Egyptian opposition movement that has led nationwide protests against President Mohammed Morsi, has given him until Tuesday to resign.
A statement issued by Tamarud (Rebel) said President Mohamed Morsi would face a campaign of civil disobedience if he did not leave power and allow elections to be held.
The group said it had collected more than 22 million signatures in support.
The crowds seen in Tahrir Square in the capital, Cairo, on Sunday were the biggest since the 2011 revolution.
In sporadic outbreaks of violence, at least one person was reported killed in an attack on the headquarters of Mohamed Morsi’s Muslim Brotherhood in Cairo, while four more died in the central province of Assiut.
Protesters across Egypt have accused the president of failing to tackle economic and security problems since being elected a year ago. Mohamed Morsi’s supporters have insisted he needs more time.