Syrian government lobbied for permission for the medical evacuation
At least 400 people need to be urgently taken from Madaya for medical care, United Nations ambassadors say.
The UN has asked the Syrian government for permission to get the most vulnerable out of the starving town, where 28 people have died of hunger since the beginning of December, according to medical charity Médecins Sans Frontières (MSF).
The UN Security Council held a private meeting to discuss the situation in Madaya, where residents have reportedly resorted to eating grass and killing cats to feed themselves.
Spanish Ambassador Roman Oyarzun said the council had been told that the 400 worst-affected residents were "in a very critical situation".
He added: "If they are not evacuated tonight, the situation will be more than dramatic tomorrow".
British Ambassador Matthew Rycroft said: "The international community cannot stand by in silence while humanitarian access in Syria continues to be denied".
"Starving civilians is an inhuman tactic used by the Assad regime and their allies. All sieges must be lifted to save civilian lives and to bring Syria closer to peace".
Syria's UN envoy Bashar Jaafari said reports of starving Madayans were fabricated and he blamed "terrorists inside" the town of stealing aid.
He said: "Actually, there was no starvation in Madaya. The Syrian government is not and will not exert any policy of starvation on its own people".
US Secretary of State John Kerry says the supply of food and medicine needs to be continuous.
Pawel Kryzsiek from the Red Cross is in Madaya.
Earlier on Monday, a convoy of 44 trucks delivered food, baby formula, blankets and other supplies to the city - the first aid to reach the town for months.
Around 40,000 people have been trapped in Madaya for six months by a government blockade which has left them without aid since October.
The town, which lies about 15 miles north-west of Damascus, has been besieged since early July by the forces of Syrian leader Bashar al-Assad and allies in Lebanon's Hezbollah movement.
Aid was also allowed into the towns of Foua and Kfarya in Idlib province, under siege by rebels seeking to oust President al-Assad.
The residents of Madaya are among about 4.5m Syrians living in areas the UN says are difficult to reach.
Footage shows aid being delivered to Madaya: