Libya remains largely in chaos following the 2011 civil war, as the rebels who ousted dictator Moammar Gadhafi later formed the militias now holding the country hostage.
Interim Prime Minister Abdullah al-Thinni's challenge of the contested vote earlier this month that appointed businessman Ahmed Maiteg only will add to that.
On May 4, the Islamist-dominated parliament appointed Maiteg as al-Thinni's successor in a disputed vote amid a walkout by secular lawmakers.
He also said that the people will have "final word" because it's the source of legitimacy.
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Meanwhile today, two airstrikes hit the February 17 militia compound in the eastern city of Benghazi, sending a column of black smoke into the air, witnesses and a security official said.
Panicked residents fled as the militia responded with anti-aircraft fire, the official said.
The official spoke on condition of anonymity because he was not authorised to speak to journalists.
Eastern air bases have pledged their support to Hifter, who launched the offensive May 16 in Benghazi.
Two days later, militias allied with Hifter stormed and ransacked the Libyan parliament in Tripoli, declaring the body suspended.
Politicians, tribes and army units have lined up with Hifter since, as thousands also have demonstrated to support him.
February 17, founded by Islamist Fawzi Abu Katef and targeted in Hifter's May 16 attack, is one of the biggest and most powerful militias in Benghazi.