Seven of the dead were killed by a shell which hit a funeral tent in the central Al-Majouri district of the eastern city, medics said.
Pro-government forces battled Islamist militiamen in the streets in several districts, an AFP correspondent reported.
Armed forces general staff spokesman Colonel Ahmed al-Mesmari said there had been “heavy fighting” as loyalists of former general Khalifa Haftar and regular army troops attacked the militias who have held the city since July.
Haftar’s air force carried out several strikes against Ansar al-Sharia targets in the city, a military source said.
The jihadist group, which is blacklisted by Washington as a terrorist organisation for its role in a deadly 2012 attack on the US consulate, is one of the two main Islamist militias in Benghazi.
Previous offensives led by Haftar had been disavowed by the Libyan government.
But its leaders have thrown their support behind the former general and rebel commander since they were forced out of the capital by Islamist militia in August.