Calling for "urgent international action" to protect civilians, Zeid also slammed what he called an "epic failure of global diplomacy" to end the seven-year-old war.
"The past week has been one of the bloodiest periods of the entire conflict, with wave after wave of deadly airstrikes leading to civilian casualties in areas of Eastern Ghouta and Idlib," Zeid said in a statement.
According to the Geneva-based UN Human Rights Office, at least 277 civilians were killed last week including 230 in air strikes by Syrian government and allied forces, the statement said.
Another 812 civilians were injured, it said.
"The no-holds-barred nature of this assault is evidenced by reports that at least nine medical facilities, six of them in Idlib and three in Eastern Ghouta, were hit by air strikes," the statement added.
"After seven years of paralysis in the Security Council, the situation in Syria is crying out to be referred to the International Criminal Court, as well as for a much more concerted effort by states to bring peace," the statement said.
"The conduct and management of this war has been utterly shameful from the outset, and the failure to end it marks an epic failure of global diplomacy."
The UN Security Council is currently examining a draft resolution calling for a 30-day ceasefire in all of Syria to enable the urgent delivery of humanitarian aid, according to a text seen by AFP yesterday.
The Council is expected to begin debate on the resolution Monday.
The position on the resolution of Syria's ally Russia was not yet known.
Earlier this week the Council failed to back an appeal by UN aid officials for a month-long pause in fighting after Russia rejected the proposal.