The city's governor, Talal al Barazi, said the extension would allow the evacuation of the remaining civilians.
He added a total of 1400 people had been evacuated from the besieged Old City since last Friday when the UN-brokered ceasefire began. Of those, 220 were still being detained for questioning.
While women and children have been free to leave, males aged between 15 and 55 are deemed of fighting age by the Syrian authorities and are being vetted by the security forces.
The move came as Russia presented draft UN Security Council resolutions on humanitarian aid access and the fight against "terrorism" in Syria.
Moscow's calls for a resolution condemning acts of "terrorism" are in tune with rhetoric from Damascus, which uses the term to describe all those fighting to oust President Bashar al Assad.
Russian Foreign Minister Sergei Lavrov said: "Terrorism is certainly no less acute a problem than the humanitarian crisis."