Zeid Ra'ad Al Hussein says "deliberate starvation" is being used as a weapon of war.
A U.S.-Russia brokered cessation of hostilities has been in place since Saturday.
With Turkey and Saudi Arabia reluctant to send forces, the war may move well beyond Syria's borders.
Aid group says that up to 40 percent of the victims were women and children.
A new report shows that 11.5 percent of Syrians have been physically affected by the war.
Russian and Syrian government forces attack rebel-held areas around the Syrian city.
The school bombing came after heavy clashes between the Syrian government and opposition forces in Aleppo province.
Around 95 percent of Aleppo's doctors have been killed or detained, or have fled the city.
According to a new report, almost all the city's physicians have fled, been killed or been detained during Syria's civil war.
Chemical weapons experts say mustard gas was used in a Syrian town where ISIS was battling a rebel group.
"If the international community had instituted the no-fly zone, Aleppo would be free today."
Putin spoke a day after Assad made a surprise visit to Moscow for talks with the Russian leader.
Government troops and their allies backed by Russian jets have launched an offensive against rebels near Aleppo.
The offensive builds on over a week of ground attacks launched with Russian air support.
Gains by ISIS north of Aleppo would threaten the supply lines of rival rebels inside the city.