Syria's state-run news agency says at least eight civilians have been wounded by rocket and mortar shells that struck several neighborhoods in the capital Damascus.

Thursday's early morning barrage comes after a rebel commander warned he would shower the capital with mortar shells to avenge government airstrikes on nearby rebel-held suburbs over the past week.

Zahran Alloush warned that Damascus would become a "security zone" as of Wednesday and until further notice.

The shelling on Thursday hit several upscale districts, including al-Malki, Abu Rummanah, Kfar Sousseh and Mazzeh.

The Britain-based Syrian Observatory for Human Rights said at least 38 rockets were fired on Damascus Thursday, adding that a number of people were wounded.