A ceasefire between the Syrian Government and rebel forces collapsed last month and fighting has since intensified in Aleppo, where more than 250,000 civilians are trapped.
The Syrian air force push to capture the rebel-controlled areas of the city has Russian and Iranian support and there are reports of thousands of civilian casualties.
Staffan de Mistura, the United Nations envoy to Syria, this week warned that rebel-held eastern Aleppo could be totally destroyed by the end of the year.
Van Bohemen told the Security Council that De Mistura had "warned us we face a situation not dissimilar to those in Rwanda and Srebrenica, atrocities this Council signally failed to prevent".
"We must learn our lessons. We must stop the destruction of the entire city of eastern Aleppo," van Bohemen said.
"Terrorism is a scourge to the world, but it is not acceptable that Russia and Syria use counterterrorism as a pretext for a large-scale bombing campaign for which civilians are paying the greatest price."
It was New Zealand's turn to hold the presidency of the Security Council last month, during which Prime Minister John Key travelled to New York, where he chaired a heated Security Council debate on the Syria crisis.