Brokered by Russia and Turkey, the withdrawal had been expected to begin shortly after dawn, with green buses ferrying militants and residents who wished to leave out to other rebel-held areas.
It would mark a key milestone in Syria's more than five year war, potentially ending the violence in one of the most intense and bloody battles of the conflict.
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But residents said Wednesday that the buses remained grounded and although the evacuation plan was supposed to be accompanied by a ceasefire, people inside east Aleppo said that by late morning, shelling had resumed.
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"The shelling started again, and bullets," said Monther Etaki, a journalist in the area. The Syrian Observatory for Human Rights, a monitoring group, also said its monitors had witnessed a large explosion in the Salah al-Din district.
There was no immediate official explanation for the delay from the government, or from the deal's sponsors. Rebels, speaking on condition of anonymity because they were not authorized to speak to the press, believed the hold-up related to disagreements between Russia and Iran, both key backers of Syrian President Bashar Assad.
After a month-long offensive, government loyalists have surrounded the rebels, leaving them clinging to a tiny pinprick of territory without functioning rescue or hospital operations.
As news of the delay broke, France insisted the U.N.'s involvement was crucial to ensuring an orderly process.
The United Nations said Wednesday confirmed that it was "not involved" in plans to evacuate fighters and civilians from eastern Aleppo, but it was ready to help.
With the tide of Syria's war turned firmly in Assad's favour, pockets of resistance across the country have been forced - often through starvation sieges - into surrender deals that culminate in local fighters boarding the now-famous green buses and heading to the northern province of Idlib.
The evacuation of Aleppo's rebel-held east would be the largest of its kind, and the biggest victory to date for Assad in a conflict that has smashed much of the country and left hundreds of thousands of people dead.
When rebel forces rode into Aleppo's eastern districts in 2012, they hoped to take the whole city - Syria's second, and a key economic hub - and turn it into a seat of power to rival the capital, Damascus. Its loss leaves the rebels without a single strategically significant area of the country and no real bargaining chip to try to force the government into a negotiated settlement.
In east Aleppo, tens of thousands of residents held out amid a blistering bombardment. On Tuesday night, many braved a heavy storm to sleep in the street as they had fled from other areas and had nowhere to stay.
