The government last week resumed its drive to retake the east of the city, where more than 250,000 civilians have been trapped under siege for months, with dwindling food and fuel supplies.
It has pounded the east with air strikes, barrel bombs and artillery fire for more than a week, killing more than 140 people as it advances.
Recapturing the east would give President Bashar al-Assad's government perhaps its most important victory yet in a conflict that has killed more than 300,000 people since March 2011.
The government has long accused rebels in the east of using residents as "human shields" and preventing them from leaving.
On Wednesday, the Syrian Observatory for Human Rights, a Britain-based monitoring group, said dozens of civilians had tried to flee overnight but were forced back by gunfire.
"On Tuesday night, around 100 families gathered near a passage from the (rebel-held) Bustan al-Basha district to cross to Sheikh Maqsud," said Observatory director Rami Abdel Rahman.
"But when the civilians tried to cross to the other side, gunfire broke out," he told AFP without elaborating.
Sheikh Maqsud is a northern neighbourhood controlled by Kurdish forces, allied with neither the regime nor the rebels.
- 'Regime rumours' -
The governorate running western Aleppo city said on its Facebook page that 10 people had crossed from the east on Tuesday evening, pledging that all arrivals "would receive the attention and care of the state."
The statement said the arrivals accused rebels of preventing people from leaving, but gave no details on how or where the civilians crossed over.
On Tuesday, the army issued a statement accusing rebels of holding civilians as "hostages."
"Permit those citizens who want to do so to leave, stop using them as hostages and human shields, clear the mines from the crossings identified by the state," it said.
Rebel groups deny any coercion and say the regime is lying.
"This has nothing to do with reality," said Yasser al-Youssef, from rebel group Nureddin al-Zinki.
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"The regime is spreading rumours to try to undermine the resolve of the rebels and those who support them in Aleppo," he told AFP.
The Syrian army, backed by allied forces from Iran, Russia and Lebanese militant group Hezbollah, launched a renewed assault on east Aleppo on November 15.
The offensive has so far killed at least 143 civilians in the east, among them 19 children. Rebel fire has killed 16 civilians in the government-held west, including 10 children.
After days of ferocious bombardment, regime troops now control half of the strategic Masaken Hanano district in the northeast of the city, the Observatory said.
Capturing the district would give the army line-of-fire control over several other parts of east Aleppo while dividing it in two.
- 'Moral outrage' -
The renewed bloodshed has stoked international concern, though there has been little sign so far of a plan to halt it.
French Foreign Minister Jean-Marc Ayrault said on Wednesday that backers of Syria's moderate opposition would meet in Paris in early December to discuss the situation.
He urged the international community to "stop averting its gaze" from the "terrible reality" of the conflict.
Save the Children called for an internationally monitored ceasefire to allow aid into east Aleppo and the evacuation of sick and wounded civilians.
"It is a moral outrage that the death toll of Aleppo's children continues to grow and seems only set to get worse, whilst so little action is being taken to end the bombing and hold warring parties accountable," said the charity's Syria director, Sonia Khush.
The latest government offensive has hit hospitals and rescue centres, and forced schools to close.
Medical officials in the east said some of the barrel bombs dropped by the government appeared to contain chlorine gas.
Both Damascus and its ally Moscow have strongly denied any illegal military use of the chemical.
Over the weekend, UN envoy Staffan de Mistura floated a humanitarian plan for Aleppo as well as a proposal for a truce.
The truce deal would have allowed the opposition administration in east Aleppo to remain in place, at least temporarily, in return for jihadist fighters leaving.
But the government rejected it, insisting the state had to retake control as any alternative would "reward terrorists."