But that plan looked in jeopardy on Thursday as LNA forces took Gharyan, about 80 km south of the capital after skirmishes with forces allied to Tripoli-based, UN-backed Prime Minister Fayez al-Serraj.
The Libyan National Army, led by Khalifa Haftar, says it has now advanced into the southern outskirts of the capital Tripoli, where the United Nations -backed government is located.
Earlier reports said forces aligned with Haftar, who is primarily backed by Egypt and the United Arab Emirates (UAE), captured the former Tripoli International Airport and several areas south of Tripoli.
On Friday, UN Secretary-General Antonio Guterres said he was "deeply concerned" over the possibility of "bloody confrontation in and around Tripoli".
He warned that they would retaliate against any threats to their forces.
Haftar, 75, was quoted by Al-Arabiya TV as telling Guterres his offensive would continue until terrorism was defeated.
Russia, which has in the past shown support for Field Marshall Haftar, called on Saturday for an end to the fighting, with Russian Foreign Minister Sergei Lavrov calling for a Libyan political settlement while on a visit to Cairo.
Analysts also believe Haftar wants to affirm his military clout after launching successful operations in the east and the south of the country - spurred by the fact that the worldwide community failed to react to those past offensives.
The U.N. Security Council on Friday also called on Haftar to halt his advance on Tripoli, warning the military move was putting Libya's stability at risk.
After a briefing by the United Nations envoy for Libya, Ghassan Salame, the council said there can be no military solution to the conflict.
LNA forces briefly took over the ruins of a destroyed airport but were driven out by fighters from the capital, government interior minister Fathi Bachagha told Libya's Al-Ahrar television station.
"Individuals that actually pledged allegiance to Haftar switched sides when they saw the army of Haftar marching into town", said Harchaoui, a research fellow at the Clingendael Institute think tank. The LNA called on Friday for Tripoli's militias to disarm.
Pro-government militiamen from the coastal town of Zawiya, west of Tripoli, retook the base after a "short exchange of fire", a source said on condition of anonymity.
Reporting from the French coastal city of Dinard, where G7 foreign ministers were meeting to prepare for a grouping summit in August, FRANCE 24's Robert Parsons said there appeared to be unity amongst the worldwide community on the need to make sure Haftar "toes the line".
Hifter is allied with the east-based administration at odds with the UN-backed government based in Tripoli.
Almost 150 of his soldiers and dozens of vehicles were captured by pro-government forces on Friday as they tried to join the offensive towards Tripoli.
Amid growing global alarm, the Group of Seven (G7) - a bloc comprised of Canada, France, Germany, Italy, Japan the United Kingdom and the United States - issued a statement on Friday saying there was "no military solution to the Libyan conflict".
"The situation should be resolved peacefully", Kremlin spokesman Dmitry Peskov said.