The offensive by Khalifa Haftar against those he describes as "terrorists" is considered "an action outside state legitimacy and a coup d'etat," the army, government and parliament said in a joint statement.
"All those who took part in this coup bid will be prosecuted," said Nuri Abu Sahmein, the head of the General National Congress, interim parliament, reading from the joint statement on state television.
Interim prime minister Abdullah al-Thani, who has branded Haftar's forces as "outlaws", and armed forces chief of staff Abdessalam Jadallah al-Salihin, who has denied any army involvement in the Benghazi clashes, were shown on television standing next to Sahmein.
Haftar, who defected from the army of Moamer Kadhafi in the late 1980s, led ground forces in the NATO-backed 2011 uprising that toppled and killed the veteran dictator.
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He now heads a group calling itself the "National Army," which launched yesterday's operation to flush "terrorists" out of Benghazi, according to his spokesman Mohammed al-Hijazi.
The army says that he is being supported by tribes, officers who defected from the army as well ex-rebels who are opposed to the central government.
That video sparked rumours on social media that a coup might be in the offing.
But the government, which has come in for criticism for failing to defeat lawlessness in Libya, was quick to quash the rumours and insist it was in control.
Libya has been rocked by lawlessness since the 2011 uprising, and authorities have struggled to assert their control over the vast, mostly desert country, which is awash with heavy weapons and effectively ruled by a patchwork of former rebel militias.