Both the UN-backed GNA government in Tripoli and the east-based parliament supported by military strongman Khalifa Haftar have announced a cease-fire in the restive region. The GNA has also called for elections in March.
Libya's neighboring warring rival governments on Friday announced an immediate nationwide cease-fire.
Prime minister of the Tripoli-based Government of National Accord (GNA), Fayez Sarraj, said he had instructed aligned forces to observe an immediate ceasefire and end all combat operations across the oil-rich country.
The international-backed government also called for demilitarizing the strategic city of Sirte, which is controlled by rival forces. Tripoli also announced that parliamentary and presidential elections will be held in March next year.
In a separate statement, Aguila Saleh, speaker of the eastern-based House of Representatives, also called for a cease-fire. That Parliament has the backing of military strongman Khalifa Haftar.
Both rival administrations said they want an end to an oil blockade imposed by Hafter earlier this year and called for oil revenues, Libya's primary source of revenue, to flow into the bank account of the National Oil Corporation outside the country.
The announcements came amid fears of escalating violence in the more than 9-year-old conflict. Both sides were mobilizing to fight over Sirte, also a major oil export terminal.
The UN's top official to Libya, Stephanie Williams, urged "all parties to rise to this historic occasion and shoulder their full responsibilities before the Libyan people."
Egyptian President Abdel Fattah al-Sisi, whose government has been a supporter of the eastern-based administration, hailed the ceasefire declarations.
"I welcome statements by Libya's presidential council and the House of Representatives calling for a cease-fire and halting military operations in all Libyan territory," Sisi said in a tweet, adding that the ceasefire is an "important step" to restoring peace to the region.
The North African nation plunged into chaos in 2011 after NATO-backed rebels overthrew former president and long-time dictator, Moammar Gadhafi.
Libya has since been divided between GNA forces ruling in Tripoli and Haftar's LNA forces dominating the east.
Turkey, Qatar and Italy support Sarraj's Tripoli-government and GNA forces. Haftar's eastern-based forces are supported by the United Arab Emirates, Egypt, France and Russia.
On a surprise visit to Tripoli on Monday, German Foreign Minister Heiko Maas had warned Libya faces a "deceptive calm" since fighting eased around Sirte.
mvb/rt (AP, AFP, Reuters, dpa)