A ceasefire was declared in Aleppo on Tuesday and buses brought in to ferry people out of the devastated enclave, the BBC reports.
But fighting resumed on Wednesday. Syrian activists also say air strikes over rebel-held territory have resumed.
The breakdown of the deal, brokered by Russia and Turkey, is being attributed to demands from the Syrian government.
It is said to be seeking the evacuation of its own injured fighters and civilians from nearby towns encircled by opposition forces.
Eastern Aleppo has been held by the rebels since 2012. But they have been squeezed into ever smaller areas in recent months by a major government offensive, backed by Russian air power.
In recent days government troops have made sweeping gains, confining the rebels to a small pocket of the city.
Late on Tuesday, Russian UN Ambassador Vitaly Churkin told an emergency session of the UN Security Council that “military actions in eastern Aleppo are over”.
Under the evacuation deal, civilians and rebels from eastern Aleppo were to be allowed to go to rebel-held areas in northern Syria.
Evacuations had been due to start at 05:00 (03:00 GMT), but did not go ahead. Fresh shelling was reported several hours later.
“The clashes are violent and bombardment is very heavy… it seems as though everything (the ceasefire) is finished,” Rami Abdulrahman, director of the British-based Syrian Observatory for Human Rights (SOHR) monitoring group, said.
The SOHR also said aircraft had resumed bombing in rebel-held areas.
Activists and civilians told the BBC parts of eastern Aleppo had been shelled. Ibrahim Abu-Laith, a spokesman for the White Helmets volunteer rescue group, said more than 40 people were injured.
One resident, Zohair, told the BBC there was total chaos. “We don’t know how many casualties there are and if there is anyone to help them.”
Russia – Syria’s ally – said the Syrian army resumed firing after the rebels broke the truce. Syrian TV reported rebel rocket fire on government-held parts of the city and said at least six people had been killed.
Russian Foreign Minister Sergei Lavrov said he expected “the rebels will stop their resistance in the next two to three days”.
Turkish President Tayyip Erdogan, meanwhile, accused Syrian forces of breaking the ceasefire deal and called the situation in Aleppo “very fragile”. He said civilians had to be allowed to leave.
He planned to speak to Russian leader Vladimir Putin later in the day, he said.
There have also been reports of atrocities. On Tuesday the UN said it had received reliable evidence of summary executions taking place, saying that in four areas 82 civilians were killed by pro-government forces. It said that many more may have died.
Syria’s government and Russia said the allegations were untrue.