Video footage distributed by Shahba Press, a network of activists in the region, showed men covered in dust carrying a woman through a destroyed street in the rebel-held Sukkari neighbourhood.
Other men carried out a baby and an older child, all survivors of the bombing.
The Observatory, a Britain-based group relying on a network of activists and other witnesses inside Syria, called on "the international community, the UN secretary general and anyone with a conscience to take immediate action to stop these indiscriminate killings of Syrian civilians."
Aleppo has been divided into regime and rebel-held enclaves since the opposition launched a massive offensive in July last year.
Rebel areas have since suffered frequent bombardment, but an activist in Aleppo told AFP via the Internet that the latest attacks are unprecedented.
"The past 10 days in Aleppo have been the most violent in the whole of the Syrian revolution," said Mohammad Wissam, a 19-year-old activist.
"When the planes come, people freeze, they stand, look up at the sky, and wait for the bombing, feeling helpless.
"Then when the bombing starts, so does the panic. People run aimlessly in all directions, looking for anywhere to hide, but there is nowhere to hide. So many people are getting trapped under the rubble of collapsing buildings," Wissam told AFP.
"When the helicopters start launching the TNT-packed barrels, it's like madness grips everyone... The bombing is random."
The opposition National Coalition has said it will boycott peace talks slated for January if the bombing of Aleppo does not cease.
"In order for the political process to succeed, immediate confidence building measures must be enacted -- to include the establishment of humanitarian corridors to cities under siege by Assad's militias -- and an immediate halt to the regime's barrel bomb campaign," Munzer Aqbiq, an adviser to the Coalition's presidency, said Tuesday.
Rights groups have widely condemned the use of TNT-packed barrels dropped from helicopters as unlawful because they fail to discriminate between civilians and combatants.
But a security source in Damascus on Tuesday defended the military's operations to "save Aleppo."
"We do not target any area unless we are 100 percent sure that the ones there are terrorists," the source said, using the regime's term for the rebels.
"The bodies you see on television are the bodies of terrorists and mercenaries, most of whom travelled into Syria from abroad."
Washington 'looks only with one eye'
Syria's state news agency SANA also defended the military's actions, accusing the United States of "ignoring the crimes committed by the terrorists" after Washington condemned the bloody air campaign in Aleppo.
"Washington is a pirate that only looks with one eye," said the agency.
SANA also reported that four people were killed in a "terrorist" mortar attack on the eastern edge of Damascus.
A foreign ministry source meanwhile accused rebels of recently attacking two sites where chemical arms are stored, one in Damascus province, the other at an unspecified location in central Syria.
Blaming foreign backers of the opposition for the attacks, the source called on the United Nations and the Organisation for the Prohibition of Chemical Weapons to "make every possible effort for these irresponsible countries to stop their practices."
The OPCW has been working in Syria since October to eliminate its massive chemical stockpile as part of an unprecedented UN-backed mission to disarm a country torn apart by civil war.
The UN resolution followed a US-Russian deal that averted US strikes on the regime after Washington accused it of launching a gas attack on August 21 that killed hundreds.