Khalifa’s rebel forces have been losing ground since UN-backed Libyan forces, assisted by Turkey, intensified a counter-offensive.
The offensive drove Khalifa forces out of the fringes of Tripoli and its airport.
Forces loyal to UN-backed government advanced further south, capping the sudden collapse of his 14-month offensive on the capital.
Military sources in Haftar’s Libyan National Army (LNA) said their forces had withdrawn from the town of Tarhouna towards Sirte, far to the east, and al-Jufra airbase in central Libya.
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And now Sirte, Ghadafi’s hometown is reportedly under attack by the government in Tripoli.
The advance extends the control of the Government of National Accord (GNA) across most of northwest Libya, reversing many of Haftar’s gains from last year when he raced towards Tripoli.
The GNA gains could entrench the de facto partition of Libya into zones controlled by rival eastern and western governments whose foreign backers compete for regional sway.
The GNA is backed by Turkey, while Haftar, whose LNA still controls the east and oil fields in the south, is supported by Russia, Egypt and the United Arab Emirates.
Sisi, who was also accompanied in Cairo by eastern Libyan parliament head Aguila Saleh, said the plan included a call for negotiations in Geneva and for the exit of all foreign ceasefire fighters from Libya.
Libya has had no stable central authority since its leader, Muammar Gaddafi was overthrown by NATO-backed rebels in 2011.
For more than five years it has had rival parliaments and governments in the east and the west, with streets often controlled by armed groups.
Sisi’s announcement comes after the abrupt collapse of a 14-month offensive by Haftar’s Libyan National Army (LNA) to try to take control of the capital, Tripoli.
Haftar is said to be a deeply divisive figure whose offensive upended a U.N.-led peace process.
It is unclear how much traction any initiative proposed by him or his allies could gain.
AFP