The internationally-recognised government of Prime Minister Fayez al-Serraj's has managed to resist the LNA march in the southern suburbs with help from from western Libyan militia.
A draft resolution is circulating to members of the United Nations Security Council demanding a ceasefire in Libya.
The move follows deadlock over how to respond to the violence that has seen at least 170 people killed and 18,000 more displaced.
Hifter's move has raised fears of a prolonged civil war similar to that playing out in Syria.
The 15-member panel informally called for an end to fighting on April 5, but progress on an official resolution stalled amid disagreements over attribution of blame.
- additional reporting Telegraph Group Ltd
