Sweden and Kuwait presented the measure that would also demand an immediate end to sieges, including in Eastern Ghouta where a bombing campaign by government forces has killed more than 240 civilians in five days.
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.
Russian Ambassador Vassily Nebenzia said it was "not realistic" to impose a ceasefire because armed groups fighting Syrian President Bashar al-Assad's forces were unlikely to uphold it.
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Russia has repeatedly blocked action in the council that would target its ally in Damascus.
Diplomats said it was unclear whether Russia would resort to its veto to block the draft resolution proposing the 30-day truce.
The measure would demand that all parties in Syria allow medical evacuations 48 hours after the start of the humanitarian pause and that UN aid convoys be authorized to make weekly deliveries to civilians in need.
It calls on all parties to "immediately lift the sieges of populated areas" and that they "cease depriving civilians of food and medicine indispensable for their survival."
UN aid officials accuse the Syrian government of blocking all aid convoys to besieged areas since January.
Western powers have expressed alarm over the government's bombing campaign in rebel-held Eastern Ghouta, where 400,000 people have been living under siege since 2013.
The draft resolution expresses "outrage at the unacceptable level of violence escalating in several parts of the country," in particular in Eastern Ghouta and Idlib.
Sweden and Kuwait, two non-permanent council members, are leading efforts to address the humanitarian crisis in Syria at the top UN body.
More than 13.1 million Syrians are in need of humanitarian aid, including 6.1 million who have been displaced within the country during the nearly seven-year war.
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