A convoy of ambulances was sent to the bomb-ravaged area after a ceasefire appeared to hold.
The International Committee of the Red Cross said around 200 casualties, including some who are critically injured, were being rescued.
Opposition fighters and thousands of civilians also left the last bastion of resistance in the northern Syrian city as part of a ceasefire deal mediated by Turkey and Russia.
World Vision's Angela Hudelston is working in the region and told Premier's News Hour: "The amount of despair that we're seeing at the moment, the amount of men crying, and Syrian men tend to be very staunch and proud men, just really shows just how much despair and desperation they have."
She told the News Hour that many of the people being assessed by aid workers needed psychological help after more than five years of bombing.
"Very distraught is the best way to describe it, their emotional state is something we're very concerned about," she added.
The UN and international aid agencies insist there are still people in eastern Aleppo waiting to be evacuated.
Russia said that more than 9,500 people, including more than 4,500 rebels and 337 wounded, have been taken out of the rebel-held districts in eastern Aleppo.
The Russian military also says some die-hard militants have stayed behind and are firing on the Syrian government troops.
Angela Hudelston speaking to Premier's Antony Bushfield:
