Libyan forces allied with the government rejected calls for a ceasefire put forward by Egyptian President Abdel Fattah al-Sissi over the weekend.
The proposal also backed by rebel Libyan commander General Khalifa Haftar includes an immediate ceasefire and aims at paving the way for elections.
It comes on the heels of major losses by Haftar's eastern forces at the hands of the UN-backed Government of National Accord, based in Tripoli.
The proposed truce underscores the shifting balance of power on the ground, says Tim Eaton, senior research fellow at the Chatham House think tank in London.
"Effectively, this call for a ceasefire is to freeze the situation and to prevent further advances from Western-based forces," he told Euronews in a live TV interview.
For the past year, Haftar has been on an offensive to capture Tripoli from forces loyal to the UN-supported government of national accord (GNA).
But the GNA, backed by Turkey, gained the upper hand last week after retaking the capital's airport, all main entrance and exit points to the city and a string of key towns nearby.
Egypt's proposal, announced by President Abdel-Fattah el-Sissi on Saturday, envisaged a cease-fire starting Monday.
The militias fighting to defend Tripoli swiftly rejected it, instead pushing eastward toward the coastal city of Sirte, a former Islamic State stronghold captured by Haftar’s forces in January.
"Clearly, they (the GNA) see the opportunity to have further advances and push eastern-based forces back further," said Eaton.
"We're witnessing a real shift in the power balance here, both locally between these actors and internationally between those powers who are supporting the rival factions," he added.
Haftar’s east-based forces are backed by the United Arab Emirates and Egypt, as well as France and Russia. The Tripoli-based government receives aid from Qatar, Italy and Turkey, which stepped up its military support in recent months, helping shift the tide of the conflict.
The UN support mission in Libya said the fighting over Tripoli "has proven, beyond any doubt, that any war among Libyans is a losing war."
It urged both sides to "engage swiftly and constructively" in UN-brokered talks aimed at reaching a lasting cease-fire agreement, and to comply with an international arms embargo on Libya.
Libya has been in turmoil since 2011, when a civil war toppled longtime dictator Muammar Gaddafi, who was later killed.