"This is an important moment that I had often looked forward to in recent years: a moment to declare an initiative that, if honest intentions prevail, will usher in a new phase in Libya's return to a normal and safe life", Egyptian President Abdel Fattah El Sisi said in televised comments.
Sisi, who was also accompanied in Cairo by eastern Libyan parliament head Aguila Saleh, said the plan included a call for negotiations in Geneva, then the election of a leadership council, the disbanding of militias and the exit of all foreign fighters from Libya.
"This initiative calls for respecting all worldwide efforts and initiatives by declaring a ceasefire from 06:00 (04:00 GMT) Monday June 8, 2020", Sisi said during a press conference.
On Thursday, the Government of National Accord said it had retaken the whole of Greater Tripoli, finally beating off an offensive Haftar's forces launched in April previous year.
El-Sisi urged worldwide support for the initiative and called on the United Nations to invite Libya's rival administrations for talks.
The proposals also called for a ceasefire to go into effect on Monday morning, the withdrawal from Libya of "foreign mercenaries" and the disarming and dismantling of militias.
Egypt's president has announced an initiative to end almost a decade of civil war in Libya, backed by the main commander in the oil-rich country's east, whose siege of the capital, Tripoli collapsed this week.
Forces allied with the Tripoli government said Friday they have retaken another key western town from rivals behind a year-long offensive on Tripoli.
"The air force has carried out five strikes in the outskirts of Sirte", slain dictator Moamer Kadhafi's hometown and the last major settlement before the traditional boundary between Libya's west and east, GNA spokesman Mohamad Gnounou said.
"Orders have been given to our forces to begin their advance and to systematically attack all rebel positions".
Sirte was taken by Haftar's forces virtually without a fight in January after one of Libya's myriad local militias switched sides.
Libya plunged into chaos in 2011 when an uprising toppled and later killed longtime leader Muammar Gaddafi. The country has since been divided into rival administrations in the east and west, with a multitude of armed groups supporting each.
But last month, as Haftar's losses mounted, the GNA said Wagner Group fighters had withdrawn from combat zones south of the capital.
His LNA forces have in recent weeks lost crucial ground to GNA forces, which are backed by Turkey.
Sisi's announcement comes after the abrupt collapse of a 14-month offensive by Haftar's Libyan National Army (LNA) to try to take control of the capital, Tripoli.
"The Emirates declares its support for the good Egyptian efforts calling for an immediate ceasefire in Libya", the Ministry of Foreign Affairs and International Co-Operation said in a tweet.