"At least 12 people have been killed and 10 others wounded since Wednesday morning during the clashes" between forces loyal to a prominent former general and Islamist groups, said the source, who requested anonymity.
For its part, the Benghazi Medical Centre gave a toll of nine dead, including three soldiers.
That figure included a father and his three children, killed when gunmen attempted to arrest a member of the family they accused of belonging to Ansar al-Sharia, one of the Islamist groups that control Benghazi.
The violence came after forces loyal to former general Khalifa Haftar, including civilians, launched a new bid to retake Benghazi.
A spokesman for Haftar, Mohamed Hijazi, said his forces had captured the headquarters of the "February 17 Martyrs Brigade," another Islamist group, after several hours of combat.
There was no way to independently verify the claim.