In a video speech to the UN Human Rights Council in Geneva, Switzerland, Zeid Ra'ad Al Hussein said armed opposition groups are firing mortars into neighborhoods of western Aleppo, but "indiscriminate airstrikes across the eastern part of the city by government forces and their allies are responsible for the overwhelming majority of civilian casualties."
He said these violations constitute "war crimes," and "if knowingly committed as part of a widespread or systematic attack directed against civilians, they constitute crimes against humanity."
The forces of Syrian President Bashar al-Assad, backed by Russian warplanes, have been pummeling eastern Aleppo as they seek to wrest it from rebel control.
However, a Russian-declared "humanitarian pause" began Thursday, which Russia said would allow rebels and civilians to leave rebel-held sections of the city during daytime hours for three days.
The Russian Defense Ministry unexpectedly announced
the pause Tuesday after a weeks-long bombardment of the Syrian city. The airstrikes and the rising death toll have received fierce criticism from Western powers.
Medical evacuations canceled
Meanwhile, the United Nations said it had canceled plans Friday to begin medical evacuations from eastern Aleppo after failing to get the necessary security assurances.
"We cannot begin safe, secure and voluntary evacuation of the sick and critically wounded and families," Jens Laerke, UN deputy spokesman for humanitarian affairs, told reporters at a briefing Friday in Geneva.
He said UN officials are assessing the situation "on a day-by-day, hour-by-hour basis" and that they "remain hopeful that all the pieces of the complicated puzzle fall into place" to start humanitarian operations.
UN officials have said hundreds of people are in need of medical evacuation from the city.
Russia said it has set up several humanitarian "corridors" for civilians and rebels to leave Aleppo.
But residents who have spoken to CNN said nobody has really taken advantage of the opportunity to leave, largely out of mistrust.
"I haven't seen anyone who left Aleppo city," said Ismail Abdullah, a member of the volunteer Syria Civil Defense, or White Helmets, who dismissed the notion of humanitarian corridors as "fake" and "just lies."
Some residents held a small protest Thursday arguing they would not leave territory for which they had fought and bled. Another told CNN he would like to depart but suggested some rebels weren't allowing civilians to leave, an argument the Syrian government and Russians also were making.
'All-encompassing ceasefire' urged
The UN High Commissioner for Human Rights called for an "immediate, prolonged and all-encompassing ceasefire" in Aleppo to allow humanitarian relief to reach all those in need.
"All parties must provide assistance and free passage for all civilians wishing to flee, without any form of reprisal -- including passage across international borders," he said.
EU urges end to 'atrocities'
The European Union also issued a sharp rebuke early Friday for attacks on civilians in Aleppo.
EU leaders "strongly condemned the attacks by the Syrian regime and its allies, notably Russia, on civilians in Aleppo," European Council President Donald Tusk told reporters in Brussels, Belgium.
"The EU is calling for an end to the atrocities and an immediate cessation of hostilities. It will consider all available options if these atrocities continue."
The government siege around rebel-held Aleppo has choked off the supply of food, fuel and other daily necessities.
Airstrikes in recent weeks have killed hundreds in east Aleppo, where about 250,000 to 275,000 residents remain trapped by government troops.
Cluster bombs claim
Save the Children called Friday for an end to the reported use of cluster munitions in Aleppo, saying they posed a particular danger to children.
According to Save the Children, the Violations Documentation Center, which documents human rights violations in Syria, recorded 137 cluster bomb attacks in Aleppo from September 10 to October 10.
Cluster munitions break up into bomblets that scatter across an area at least as great as a soccer field. These bomblets, which can look like a ball or toy, often fail to explode until curious children pick them up, resulting in devastating injuries.
Rights group Amnesty International also this week cited Aleppo residents who said they had witnessed the use of internationally banned cluster munitions.
"The use of cluster munitions is banned under international law because they are inherently indiscriminate and, due to their high dud-rate, pose a long-lasting threat to civilians," said Lynn Maalouf, deputy director for research at Amnesty's Beirut regional office.
"Their apparent use in eastern Aleppo city is just further evidence of how determined Syrian government forces and their Russian allies are to create a hostile and deadly environment in the city, clearly aimed at driving civilians out at any cost."