"International humanitarian law was developed precisely to stop this type of situation, where civilians are slaughtered in droves in order to fulfil political or military objectives," he said in a statement.
Information documented by his office alone showed at least 346 civilian deaths and 878 injuries, mostly from air strikes on residential areas, since the Syrian government and its allies escalated an offensive against the rebel-held enclave on Feb. 4.
There were also 15 deaths and 51 injuries reported among civilians in and around Damascus, the result of a dramatic escalation of rebel fire on government areas.
Many of the violations may amount to war crimes, he said.
Women and children, trapped for five years of siege, were now in a state of panic, without food, sanitation, or safe havens after air strikes destroyed their homes, Zeid said.
"How much cruelty will it take before the international community can speak with one voice to say enough dead children, enough wrecked families, enough violence, and take resolute, concerted action to bring this monstrous campaign of annihilation to an end?"
The United Nations has been pleading with the Syrian government for months to arrange the evacuation of hundreds of seriously ill patients among the population of almost 400,000.
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Zeid said repeated strikes on medical facilities, which are meant to be protected by international law, meant people with extreme injuries now faced a slow and painful death.
He reiterated the world body's call for an immediate cessation of hostilities and immediate humanitarian access, as well as medical evacuations and the chance for people to leave.
But any political agreement must not include forced displacement of civilians, he said.
Syrian government forces, backed by Russian and Iranian allies, have previously used similar siege tactics to drive rebels out of major towns, including Syria's second city Aleppo.
Such tactics appear to flout international law but Russia, Syria's ally, has vetoed 11 U.N. Security Council resolutions criticising its handling of the war.