About 200 airstrikes have pummeled neighborhoods in eastern Aleppo since Friday morning, said Ammar al-Selmo, the head of the Syria Civil Defense group, a volunteer emergency medical service.
Rescue teams are still working to extract people from the rubble, he said.
Al-Selmo estimated that more than 100 people have been killed and hundreds more injured within Aleppo neighborhoods by the airstrikes. This figure does not include neighborhoods in the countryside. CNN could not immediately confirm the death toll.
During a rescue operation overnight Friday into Saturday, at least five members of the Syria Civil Defense, also known as the White Helmets, were injured by a nearby airstrike, al-Selmo said. One of those hurt is in critical condition.
An activist with the opposition-aligned Aleppo Media Center, Mujahed Abu Aljood, told CNN on Friday that more than 60 airstrikes rained down that day.
He said the center believed more than 50 people, including children, were trapped in rubble in different areas of Aleppo.
"Civil defense crews are incapable of extracting them from underneath the rubble due to the intense airstrikes on the city of Aleppo," he said. "Since midnight until now, there are eight dead people and 10 injured as a result of the airstrikes."
The AMC cited the Syria Civil Defense as saying that Russian jets were involved in an airstrike north of Aleppo; CNN has reached out to Russian authorities for comment, but has yet to receive a response.
United Nations takes a stand
United Nations Secretary-General Ban Ki-moon warned that the Syrian offensive's airstrikes, incendiary weapons and bunker-buster bombs in densely populated places may amount to war crimes, the Ban's spokesman said Saturday.
"The secretary-general is appalled by the chilling military escalation in the city of Aleppo, which is facing the most sustained and intense bombardment since the start of the Syrian conflict," the statement said. "The secretary-general considers this a dark day for the global commitment to protect civilians."
The secretary-general urged the international community to unite and say it will not tolerate the indiscriminate use of power weapons against civilians.
Rebels launch counterattack
Syrian rebels, meanwhile, launched a counter-offensive against government forces Saturday to try to retake the area north of the city that was lost to the government earlier in the day, according to the UK-based Syrian Observatory for Human Rights (SOHR).
There were conflicting reports as of late Saturday about the success of the counterattack.
The fragile ceasefire that went into effect on September 12 fell apart less than a week later after US-led coalition forces struck a Syrian position
, killing scores of soldiers.
The US military did not dispute the strike, but characterized it as "unintentional" and relayed its "regret" to Syria through Russia.
The strike has erupted in a diplomatic row between the US and Russia
, the brokers of the ceasefire.
After an attack on an aid convoy -- which no one has admitted to carrying out -- and the new fighting, the head of the United Nations acknowledged the international community's failure.
"The Syrian tragedy shames us all," the secretary-general said. "The collective failure of the international community should haunt every member of this Council."
Speaking at the United Nations on Thursday, Russian Foreign Minister Sergey Lavrov called for an investigation of the latest violence.
"It is essential to prevent the disruption of these agreements and to carry out an unbiased and impartial investigation of the incidents," Lavrov said.
Rooting out terrorism groups in Syria, he said, "is absolutely important in order to have truces and reconciliation."
The United States has pointed its finger at the regime of Syrian President Bashar al-Assad, blaming it for the breakdown of the cessation of hostilities and demanding the grounding of all military aircraft.
US Secretary of State John Kerry called on Syria and Russia to end aerial bombardment of eastern Aleppo, stating there is "no chance" of peace without an end to military operations and coordination between the parties.
Al-Assad on Thursday said the United States is not interested in a ceasefire
, but that his government is ready and willing to commit to one.
"I believe that the United States is not genuine regarding having a cessation of violence in Syria," he told the state-run Syrian Arab News Agency.
The latest air strikes on Aleppo come after 20 people were killed and the city's main water pumping station was destroyed, according to the media center.
The military operation, conducted by Syrian forces, formally marked the end of the short-lived ceasefire that sought to quell violence, coordinate efforts to defeat ISIS and allow aid to enter the besieged city.
The UN children's agency said the damage Thursday to the water pumping station, plus the retaliatory closure of another serving the western part of Aleppo, left almost 2 million people in the city without access to running water.
"Depriving children of water puts them at risk of catastrophic outbreaks of waterborne diseases and adds to the suffering, fear and horror that children in Aleppo live through every day," said Hanaa Singer, UNICEF representative in Syria.
Syria's military announced the "start" of military operations in eastern Aleppo, warning residents to keep away from specific sites and centers of "armed terrorist groups," according to state-run news agency SANA.
Activists say allied Russian forces have participated in the strikes, though Moscow has not confirmed its involvement.
Obstacles to aid
An airstrike on Monday destroyed a Syrian Arab Red Crescent (SARC) aid convoy in Urum al-Kubra, west of Aleppo, prompting the United Nations to halt its aid operations in Syria.
Russia denied carrying out the strike, instead charging that the convoy was hit by a "terrorists' pickup truck carrying a large-caliber mortar," according to Russian state news agency Tass.
A convoy of trucks carrying humanitarian aid did reach the besieged town of al-Muadamiyah in the Damascus countryside, a UN spokesperson told CNN on Thursday. It's an interagency humanitarian effort of the United Nations and SARC, carrying aid for 7,000 people, according to a tweet from the SARC.
Syrians in eastern Aleppo and other besieged cities and towns are facing a dire shortage of food, medicine and other supplies. The country's civil war, which is in its sixth year, has so far claimed the lives of more than 400,000 people and sparked a refugee crisis, according to the United Nations.