"This initiative calls for respecting all international efforts and initiatives by declaring a ceasefire from 0600 (0400 GMT) Monday, June 8, 2020," President Abdel Fattah Al Sisi told a news conference.
Sisi was speaking alongside Haftar and his ally, eastern parliament speaker Aguila Saleh, as he unveiled "the Cairo declaration".
The initiative urged the withdrawal of "foreign mercenaries from all Libyan territory, dismantling militias and handing over their weaponry," Sisi said.
He also said it paves the way for forming an elected presidential council in Libya and prevents "extremist groups and militias" from gaining control over the country's resources.
But Sisi’s announcement came as forces loyal to Libya’s Government of National Accord (GNA) declared a fresh offensive that aims to take Sirte, the hometown of Muammar Qadhafi, in a bid to build upon a string of recent successes against Haftar’s men.
And Mohamad Gnounou, a spokesman for the GNA’s forces, appeared to pour cold water on the Egyptian proposals, asserting "we will choose the time and place when” the war ends.
Sisi urged international support for the initiative and called on the United Nations to invite Libya’s rival administrations in the east and the west for talks.
He called for the resumption of the 5+5 Joint Military Commission talks in Geneva, which kicked off early this year bringing together military officers representing the rival factions.
Sisi also warned against an "insistence” on military solutions to resolve the crisis in the neighbouring country.
Haftar expressed "support and acceptance” of Egypt’s initiative "in the hopes of obtaining international support to guarantee its success”.
The Libyan commander said Turkey’s intervention in support of the GNA "fosters internal polarisation”, urging efforts be bolstered to stop Ankara transferring fighters and weapons to Libya.
During the press conference, Saleh asserted that the declaration clears the way for a transitional period comprised of an executive authority led by a president, two vice presidents, and a prime minister.
Libya has been mired in chaos since the 2011 uprising that toppled and later killed longtime dictator Qadhafi.
Eastern-based Haftar has since last year sought to regain control over the west, fighting the GNA in an abortive attempt to seize the capital Tripoli