"During the clashes the army entered the neighbourhood of Arbaeen and conducted raids, during which they killed members of three families," resident Abu Ammar told Reuters from the city.
He said among the dead were 10 members of the Kanan family, eight from a family named Okda and three from the Saffaf family.
Another resident said the clashes continued and rebels have appealed to fighters in other parts of the city for help.
Syrian forces besieged the Arbaeen district in the early hours of Thursday, residents said, adding that the army was using mortars and tanks to attack the neighbourhood.
"We are unable to flee and many families are trapped inside their houses," a resident said.