New Zealand, one of the 10 non-permanent Security Council members, on Wednesday presented a draft resolution demanding an end to air attacks in Syria's battleground city of Aleppo.
The new measure followed the failure of the council to adopt two resolutions on a ceasefire in Syria, one of which was vetoed by Russia during a stormy meeting at the weekend.
The draft text seen by AFP "demands an immediate and complete end to all attacks which may result in the death or injury of civilians or damage to civilian objects in Syria, in particular those carried out by air in Aleppo."
It remains unclear if the proposed measure will come to a vote at the Security Council.
Council members will discuss the crisis in Syria during a luncheon meeting with Secretary General Ban Ki-moon on Wednesday, ahead of a new council session on Monday.
The United States and Russia are convening international talks in Europe at the weekend to try once again to secure a ceasefire and end the Russia-backed Syrian bombing campaign in Aleppo.
"We believe that the council has a responsiblity to address what is clearly the biggest issue on its agenda," said New Zealand's Ambassador Gerard van Bohemen.
"With the level of killing and destruction going on, just to give up seems to us to be an unacceptable course of action," he told reporters.
The move by New Zealand came as Canada was leading a push at the General Assembly to mobilize international efforts after a US-Russian ceasefire deal collapsed and the Security Council failed to take action.
The General Assembly is expected to hold a special session on Syria next week that could lead to further measures, possibly targeting Syria's voting rights at the United Nations.
Canadian Deputy Ambassador Michael Grant told AFP that the meeting would allow UN member-states to "express their anxiety and distress over what is happening in Syria and the lack of an appropriate response by the international community and the UN."
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