"A humanitarian, political and social disaster is already upon us, and what looms is truly a nightmare," Pillay told diplomats as she opened a UN Human Rights Council session in Geneva.
She warned that the rights violations in Syria had "reached horrific dimensions," describing the situation in the country as "an intolerable affront to the human conscience."
"Confronted with the flagrant disregard of international law and human life on every side, I feel utter dismay," she said, lamenting that "we in the international community are failing to meet our fundamental obligations to the victims."
Pillay said the regime was using "indiscriminate and disproportionate force in residential areas," including reports of direct targeting of schools and hospitals.
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She also decried "wanton human rights violations" by rebel groups, including extrajudicial killings and accounts that some women and girls have been forced to marry combatants.
Pillay also voiced alarm over the ongoing battle for control over the strategic town of Qusayr, near the Lebanese border, with reports that hundreds of civilians have been killed or injured and thousands may remain trapped.
"These war crimes and crimes against humanity cannot be allowed to go unpunished," she said.
Human Rights Council president Remigiusz Henczel said the council had accepted a request by the United States, Turkey and Qatar for an urgent debate on the situation in Syria and especially in Qusayr.
He ruled that the debate would be held on Wednesday.