The self-styled Libyan National Army said fighting in Soug al-Hout neighbourhood was over and its soldiers had advanced into the central district of Al-Sabri where they were surrounding the last jihadists.
LNA General Abdessalam al-Hassi told AFP the jihadists were cornered in a small part of Al-Sabri and coming under attack from air strikes as well as ground forces on three fronts.
Haftar's forces have retaken most of Benghazi since the eastern coastal city was overrun by jihadists in 2014.
Hassi said the "total liberation of Benghazi from jihadists is imminent".
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A spokesman for the LNA special forces, Colonel Miloud al-Zwei, said Haftar's forces were getting ready "to launch an assault on Al-Joumhouriya hospital and Al-Jarid market" in Al-Sabri.
Benghazi, cradle of the 2011 uprising that toppled and killed Libya's veteran dictator Moamer Kadhafi, was overrun by several jihadist groups.
These include the Revolutionary Shura Council of Benghazi, an alliance of Islamist militias among them suspected members of the Islamic state group and the Al- Qaeda-linked Ansar al-Sharia.
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