The Republic of Congo, which chairs the African Union high-level committee on Libya, has called for the meeting, just ahead of the opening of the African Union Summit in Addis Ababa on Monday.
So far, only four heads of state have confirmed: Chad's Idriss Deby, Niger's Mahamadou Issoufou, South Africa's Jacob Zuma and Mauritania's Mohamed Ould Abdelaziz.
Algeria's Prime Minister, Abdelmalek Sellal and the AU's Commissioner for Peace and Security, Smaïl Chergui will also be present.
Fayez al Serraj, the head of the internationally-recognised government of Libya will be attending, though it is not yet confirmed if Khalifa Haftar, the head of most of Libya's armed forces, will be present.
Since the fall of Libya’s leader Moamer Kadhafi in 2011, the country has been plunged into a crisis between feuding tribes and militias over who will claim leadership.
Speaking to RFI, Algeria’s Foreign Minister Ramtane Lamamra said: "The African union has been working very effectively to promote a peaceful transition in Libya at times when others have preferred a military option.
"Now is the time to look at the ill-advised consequences made by a number of non-African countries at the time and now the time has come to give us ample room to have African wisdom prevail."
Friday’s mini-summit follows from a meeting that took place on 21 January in Cairo, Egypt, with the United Nations (UN) Special Envoy Martin Kobler.