An official from the special forces loyal to the elected government said the ongoing operation in areas across the city started early today.
The official, speaking on condition of anonymity because he was not authorised to speak to journalists, said the air force is backing up the ground troops and the fighting continues.
"I hope it's the last battle but I don't think it will end today. The evil forces still have power but it's a matter of days," he said.
The toll is likely to be significantly higher. Witnesses said corpses could be seen on the streets of central Benghazi today as screams and ambulance sirens rang out.
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Area residents said the military has taken control of large portions of al-Leiti, a Benghazi district regarded as a major stronghold for the extremist militias. They say government troops were visible on the streets of central Benghazi.
The widespread militia violence has plunged Libya into chaos less than four years after a NATO-backed uprising toppled and killed longtime dictator Moammar Gadhafi.