The North African nation has been gripped by turmoil since the 2011 uprising against long-time leader Moamer Kadhafi, with the authorities struggling to control powerful militias that ousted and killed him.
Gunfire and explosions were heard in Benghazi, an AFP correspondent said, after Haftar announced he was ready to "liberate" the city.
Witnesses said tanks had launched an assault against an Islamist militia known as the "February 17 Martyrs Brigade," while warplanes carried out raids on the group, whose headquarters is located west of the city.
A spokesman for Haftar's forces said they captured the February 17 headquarters after several hours of fighting, but there was no way to independently verify the claim.
Later, the army announced it had thrown its weight behind Haftar, who launched a first, unsuccessful, campaign against the Islamists in May, dubbing it "Operation Dignity".
"The Libyan army claims 'Operation Dignity'" as one of its own campaigns, spokesman Colonel Ahmed al-Mesmari said, adding, "now it is one operation of the army, among others."
"I bring you today (a message) from the men of Operation Dignity saying that they are ready to fulfil their next goal, which is to liberate the city of Benghazi."
A spokesman for Haftar had earlier called on young people in Benghazi to secure their neighbourhoods and to keep out Islamist fighters, saying the former general's forces would enter the city on Wednesday.
The Islamists include the Ansar al-Sharia jihadist militia, which the United States has branded a "terrorist" organisation.
Haftar is a former Kadhafi general who spent years in exile before returning to join the 2011 revolution. When he launched Operation Dignity, the authorities accused him of trying to carry out a coup.
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