"We entered most of the sectors controlled by terrorist groups in Lithi" in central Benghazi, a military source told AFP.
The press office of Libya's General Command, which supports the recognised administration, said it would announce the liberation of Lithi, a bastion of Islamist militias including IS, "imminently".
Libya has had rival administrations since the summer of 2014 when the recognised government fled Tripoli after a militia alliance including Islamists overran the capital.
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Fighting has flared periodically in Benghazi as security forces try to wrest neighbourhoods from armed groups including IS and Ansar al-Sharia, which is close to Al-Qaeda.
At least 19 pro-government troops were killed over the weekend in clashes that saw loyalists seize Al-Marayseh port in western Benghazi and Al-Hawari hospital in the south.
Medical sources in Benghazi said Tuesday that more than 20 loyalist fighters had died in the operation to retake the city.
Earlier this month the military announced that one of its fighter jets had been shot down as it carried out air strikes on opposition positions in the coastal city.
Chaos engulfing Libya since the fall of dictator Moamer Kadhafi's regime in 2011 has fostered the rise of IS which has based itself in the former dictator's hometown of Sirte in eastern Libya.