"The armed forces pushed the terrorists in all directions around Tripoli and are moving towards the centre of the city," Mismari wrote on Facebook.
At the same time, the Libyan media reported that violent clashes, involving grenade launchers and artillery, in the areas of Salah al-Din, Al-Khilla, Biar Alliak, Al-Sabia on the outskirts of the Libyan capital continued.
According to the Internet portal Libya Akhbar, LNA aviation attacked the GNA forces before another attempt to storm the capital.
Libya has been suffering from unrest since 2011 when long-time leader Muammar Gaddafi was overthrown and killed. Since then the country has been split between two rival governments, with an elected parliament, supported by Haftar's army, governing the country's east and the GNA ruling the west from Tripoli.