Masked gunmen fired birdshots at the protesters camping at the Tahrir Square, injuring nine people, local media reported, saying the firing stoked tensions and violent street confrontations are expected later today when the rival rallies will be staged outside the barricaded presidential palace.
Security across the capital was tightened and police deployed anti-riot vehicles in central Cairo after the firing.
The present political turmoil began after President Mursi granted himself absolute powers through the November 22 decree that had put his decisions beyond judicial review, a move which gained him titles like "dictator" and "Pharaoh".
Mursi tried to calm protests by annulling the decree, but decided to go ahead with the December 15 referendum on a new constitution as scheduled.
Opposition parties rejected the referendum and called for massive march towards presidential palace to protest it.
So far, seven people have been killed in clashes between the Islamist Muslim Brotherhood and opposition supporters who are also besieging Mursi's presidential palace.
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In a statement after talks on Sunday, opposition National Salvation Front said it would not recognise the constitution "because it does not represent the Egyptian people".
"We reject the referendum which will certainly lead to more division and sedition," spokesman Sameh Ashour said.
The military has warned of "disastrous consequences" if the political crisis gripping the country was not resolved through dialogue and urged all political forces to pursue dialogue.