Field Marshal Tantawi, who has headed up the ruling military council since Hosni Mubarak was ousted in February, promised in a televised address that elections would take place in June next year, six months earlier than originally planned.
But Tahrir Square still swelled with tens of thousands of protesters, who chanted “Leave! Leave!” and “The people want to topple the marshal”.
The renewed unrest has resulted in 37 people dead so far.
Tantawi also said a national salvation government would be installed after the entire Egyptian cabinet resigned on Sunday. Parliamentary elections will begin on Monday as planned, though it is thought they will take until January to complete.
The marshal added: “The army is ready to go back to barracks immediately if the people wish that through a popular referendum, if need be.”
Clashes between police and protesters have showed no signs of calming. Police have used tear gas and rubber bullets to control the crowd, and hundreds have been reported injured.