Abdullah al-Thani also expressed his frustration over a lack of support from the international community, calling for foreign weapons and assistance in the fight against the Islamists.
"All military forces have been placed under army command to liberate Tripoli and Benghazi soon, inshallah (God willing)," Thani told AFP in a telephone interview from the eastern town of Al-Baida.
Since a 2011 revolution which toppled Libya's longtime leader Moamer Kadhafi, interim authorities have failed to establish a regular army and had to rely on state-backed militias.
On Wednesday, retired general Khalifa Haftar launched an operation against Islamist militias in the eastern city of Benghazi with the backing of army units and civilians who have taken up arms.
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The operation is "under the control of the regular army and the control of the government and the parliament," said Thani.
An AFP count based on hospital sources in the city put the death toll in Benghazi at 66 since Haftar's offensive began, including eight killed today and four who died in a suicide attack the previous day.
Before this week's assault, Haftar's forces had been steadily beaten back to a final redoubt at Benghazi's airport, which has come under attack by Islamists since mid-September.
Thani's government and parliament, elected on June 25, have taken refuge in the country's east to escape Fajr Libya, a mainly Islamist coalition which seized control of Tripoli at the end of August.
The fall of the capital followed a weeks-long battle with pro-government militias from the town of Zintan in western Libya.