The Security Council meeting was requested by Switzerland and Brazil - the United Nations co-leaders on the Syria humanitarian effort.
UN humanitarian affairs chief Martin Griffiths, who this weekend visited Turkey and Syria where anger over the pace of aid has swelled, said "We have so far failed the people in north-west Syria," Griffiths said Sunday on Twitter.
"They rightly feel abandoned," he said, adding that it was the international community's obligation "to correct this failure as fast as we can."
The 7.8-magnitude quake that struck Syria and Turkey on February 5 has so far killed more than 35,000 people and left communities in both countries desperate for emergency help.
Before the earthquake struck, almost all of the crucial humanitarian aid for the more than four million people living in rebel-controlled areas of northwestern Syria was being delivered from Turkey through the Bab al-Hawa crossing.
This is thanks to a cross-border mechanism created in 2014 by a UN resolution, contested by Damascus but also by Moscow, a permanent Security Council member with veto power, which has sought in recent years to reduce the number of crossings from four to one.
Aid delivery through Bab al-Hawa was interrupted by the quake but has since resumed, and calls to open other crossings are multiplying.
"People in the affected areas are counting on us," Washington's UN ambassador Linda Thomas-Greenfield said Sunday in a statement.
"We must vote immediately on a resolution to heed the UN's call for authorization of additional border crossings for the delivery of humanitarian assistance."
Malta's UN ambassador Vanessa Frazier, who chairs the 15-member Security Council this month, said members have yet to begin formal discussions on a resolution, "but I'm sure that we will."
"We are doing our job," she said, when asked about criticism that the council was acting too slowly.
"There's no point in meeting for us without the information" coming from experts on the ground, Frazier added.