After four days of violent clashes, Field Marshall Mohamed Hussein Tantawi said presidential elections would be held by July 2012.
But many protesters in the square said the concession was not enough and have demanded the field marshal step down.
Clashes continued after dark between riot police and protesters in Cairo.
Television pictures from Tahrir Square showed ambulances arriving to pick up injured people.
According to Egypt's ministry of health, at least 30 people have been killed since Saturday and hundreds injured.
Police have been using tear gas, rubber bullets and birdshot against protesters who have been throwing stones.
Some protesters said live bullets had been fired.
Clashes have also been reported in several other Egyptian cities including Alexandria, Suez, Port Said and Aswan.
Egypt's ruling military council had previously said presidential elections might not happen until late 2012 or 2013. That move, coupled with a draft constitution produced earlier in the month that would exempt the military and its budget from civilian oversight, prompted a mass demonstration in Tahrir Square on Friday.
Events turned violent when security forces attempted to remove the protesters from the square on Saturday.
Many Egyptians have become frustrated with the slow pace of political reforms since Hosni Mubarak was overthrown as president in February after a wave of mass demonstrations.
The Supreme Council of the Armed Forces (or Scaf) took charge after his ouster, promising to implement the transition to civilian rule.
Those polls, taking place over three months, are due to set in train the transition to democracy.
The military's original timetable called for the new parliament to then choose a 100-member constituent assembly to draw up a new constitution within six months.
Field Marshal Mohamed Hussein Tantawi: "We do not seek power"
A referendum would then approve the document before a presidential election was held. That would mean the military remaining in power until late 2012 or early 2013.
Protesters, however, had demanded the presidential vote take place after the parliamentary elections.