Hundreds of Damascus residents fled from clashes and army shelling of several districts of the embattled Syrian capital on Thursday, a rights watchdog reported, as the military gave them two days to get out.

The military declared residents have 48 hours to leave areas where clashes are taking place between security forces and rebels, a security source has claimed.

"These extremely violent clashes should continue in the next 48 hours to cleanse Damascus of terrorists by the time Ramadan begins," the source said, referring to the Muslim holy fasting month.

The Britain-based Syrian Observatory for Human Rights watchdog said "hundreds of people" fled several areas.

In the western district of Mezzeh, hundreds of people were on the move, "fearing a large-scale operation by regime troops", the Observatory said.

Residents also fled the southern district of Tadamon and the Palestinian refugee camp Yarmuk for an unknown destination, it added.