The medical charity MSF says more than 130,000 Syrians have fled heavy bombing in the northern Al Safira district in the past two weeks.
They are being forced to escape to areas already struggling to cope with a huge influx of displaced people, the BBC reports.
Medecins Sans Frontiers says humanitarian aid is insufficient and medical establishments are often being targeted.
In New York, the United Nations humanitarian chief Valerie Amos has told the Security Council about 2.5 million Syrians are still trapped beyond the reach of aid workers and action is urgently required.
