Turkish President Tayyip Erdogan said on Friday he was upset that Sarraj was stepping down and would hold talks on the issue with the GNA later this month.
Forces loyal to Haftar and the Libyan National Army (LNA) control the oil-rich east; meanwhile, the GNA, led by Prime Minister Fayez al-Sarraj, largely controls the west, including the capital Tripoli.
Eastern Libyan commander Khalifa Haftar announced on Friday he would lift for one month his blockade of oil output and said he had agreed with the rival Tripoli government on "fair distribution" of energy revenue.
The current blockade has deprived the National Oil Corporation of almost $10 billion in revenue and led to nationwide fuel shortages.
The blockade on Libyan oil exports imposed by one faction in the country's civil war will be lifted, potentially adding large volumes of crude to a market weakened by the coronavirus pandemic. The blockade, in the country with Africa's largest oil reserves, is estimated to have cost the National Oil Corporation (NOC) almost $10 billion (€8.4 billion) in revenue.
Neither Haftar nor Maiteeg commented on the presence of LNA and allied foreign forces in oil production and export facilities.
Haftar's statement lifting the blockade was made in coordination with the GNA's Deputy Prime Minister Ahmed Maetig.
Talks have focused on appointments to the top of the country's key institutions, with the naming of the heads of Libya's central bank, its National Oil Corporation and the armed forces the main points of dispute.
"With these meetings, God willing we will turn this issue towards the direction it needs to go", he said.
Libya has been in chaos since a Nato-backed uprising toppled and killed longtime dictator Muammar Gaddafi in 2011.
According to Bloomberg, the rival sides will be asked in Geneva to agree on a new presidential council structure that unifies the country's dueling administrations and schedule elections.
The two parties plan to discuss a demilitarisation of the city of Sirta, Libya's gateway to major oil fields and export terminals, to finally put an end to Libya's 10 year long crisis.
Since Jan. 17, foreign militia and groups loyal to the putschist Haftar - backed by Russian Federation and the UAE - have closed Libyan oil fields and facilities.