"The forces of (President Bashar) al-Assad are shooting on those taking part in the funerals and firing tear gas to disperse them," Mohammad Chami, of the Local Coordination Committees which organise protests on the ground, said when contacted via Skype.
He said it was "sustained gunfire."
The Syrian Observatory for Human Rights said there were casualties among the "thousands" attending the funerals in the Mazzeh district in the west of the city without specifying their number or severity.
The Britain-based watchdog said four people, two of them teenagers, were killed when security forces opened fire on Friday's "unprecedented" demonstrations in Damascus.
"It's the first time that the protests have spread to well-to-do neighbourhoods," said Moaz Shami of the LCC, adding that a total of 49 were counted in the capital on Friday.
Mazzeh is a strategic area of the capital that houses many embassies, as well as government, security force and state newspaper offices.
Before Friday's demonstrations, Damascus had been relatively untouched by the massive protests sweeping some provincial cities and more used to loyalist demonstrations organised by the authorities.