Khalifa Haftar, who lived in exile in the United States before returning home to lead ground forces in the 2011 NATO-backed uprising that toppled Muammar Gaddafi, heads what he calls a "National Army".
On Friday his paramilitary force, backed by warplanes and helicopters, pounded Islamist militiamen in Libya's second city and fought pitched battles with the ex-rebels.
Prime Minister Abdullah al-Thani denounced Haftar's forces as "outlaws" and called on all parties to observer restraint.
"The operation will continue until Benghazi is purged of terrorists," he told Libya Awalan television.
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Armed forces chief of staff Abdessalam Hadallah al-Salihin has denied any army involvement in the Benghazi clashes, although he admitted that some officers and army units had defected to join Haftar.
Later Haftar spokesman Colonel Mohammad Hijazi called on people living in the western Benghazi district of Guwersha and the southern one of Sidi Fradj to evacuate their homes.
The army's high command upped the ante by declaring all of Benghazi and its suburbs a "no fly zone until further notice," state-run Lana news agency said.
"All military planes flying over the city will be shot down by army units... And units of the revolutionaries (ex-rebels)," it said.
But it was not clear if the army has the means to carry out its threat, which came as local sources said mediation was underway to try and prevent new fighting in Benghazi.
A precarious calm reigned in the port city today.