The French ambassador has blamed the Syrian regime for lack of access to towns and villages
Britain, the US and France have urged the United Nations to start humanitarian aid air drops ahead of a Security Council meeting to discuss the crisis in besieged areas.
The calls came after a 1 June deadline for aid convoys to reach all areas besieged by the Syrian government passed - although land deliveries made it into Daraya for the first time since 2012 on Wednesday.
Supplies also made it into Moadamiyeh for the first time since March.
Russia's ambassador Vitaly Churkin welcomed the aid deliveries as a positive step and suggested that plans to air drop humanitarian relief could be put on hold for now.
But French ambassador Francois Delattre, who holds the council presidency this month, said access to the towns and villages under siege remained blocked and blamed the Syrian regime.
He said: "France is asking the United Nations and in particular the WFP (World Food Programme) to begin humanitarian air drops for all the areas in need, beginning with Daraya, Moadamiyeh and Madaya, where the civilian population including children risks dying of hunger."
The 20-nation International Syria Support Group (ISSG) asked the WFP to prepare for air drops if aid remained blocked, although it is unclear if the Syrian regime will allow planes carrying relief supplies into its airspace.
In Washington, US State Department spokesman John Kirby said deliveries to the two towns were "far from sufficient" and that the United States supported moving forward on plans for the air drops.
While the diplomatic wrangling rumbled on, thousands of Syrian refugees arriving in Jordan's Azraq refugee camp - and considered a security risk - have been isolated by barbed wire-topped fencing.
The Village 5 camp within a camp was set up in late March as part of a deal between Jordan and international aid agencies to speed up admissions of refugees.
Under the deal, Jordan agreed to let in about 300 Syrians a day, or five times more than before, on condition that newcomers are isolated in Azraq for more security checks.