Both Libyan figures arrived in Egypt on Sunday, within the framework of Cairo-led moves to resolve the crisis of Dabaiba's "obstinacy" in handing over power, the sources added.
Haftar announced on Tuesday he will run in a Dec. 24 presidential election that aims to help end a decade of conflict.
The statement reiterated the importance of protecting Libya's unity and sovereignty.
Ibrahim al-Faidi said Haftar's decision was meant to transport staffers and users of oil companies.
Speaker of the Libyan Parliament Aguila Saleh will visit Egypt Sunday, according to Libyan media outlets.
The Libyan National Army (LNA) Mobilization Commander Khaled al-Mahgoub affirmed that Militias affiliated with the government of National Accord were located 140 kilometers away from Sirte
Haftar added that Turkish aggression threatened the unity of Libya and the stability of the region.
Al Mesmari extended thanks to the Arab countries that backed Libya to overcome this crisis and counter-terrorism and foreign interference.
Head of the Egyptian Intelligence Service Abbas Kamel, Speaker of the House of Representatives Ali Abdel Aaal and Foreign Minister Sameh Shoukry attended the meeting.
Haftar discussed with Egyptian officials the resumption of Geneva military talks between the Libyan warring parties in the form of the "5 + 5" meeting.
Libyan National Army (LNA) commander Field Marshal Khalifa Hifter demanded Egypt's international support to stop the Turkish intervention in Libya.
Haftar announced that the general command of the armed forces accepts a mandate from the Libyan people to govern the country.
"Our patience is running thin regarding repeated truce breaches by Erdogan and Sarraj's mercenaries and their failure to fulfill their Berlin obligations," Haftar said.
Noke went on explaining that there have been certain developments regarding Libya; however, it is still early to predict what will happen.
Russia's foreign ministry said the heads of Libya's two warring factions will hold talks in Moscow on Monday, the Interfax news agency reported.
President of the European Council Charles Michel will visit Egypt this week in a tour that includes Turkey, at the time where Libyan crisis sees a stand-off.
In a press conference with the Algerian Foreign Minister, Shoukry said that both countries have strong consensus on rejection of any foreign military presence in the Libyan territories.
Foreign Minister Sameh Shoukry flew to Algeria on Thursday to convey President Abdel Fatah al-Sisi's message to Algerian President Abdel Madjid Tebboune.
The Libyan National Army forces managed on Monday to seize the city of Sirte.
The Libyan Parliament held Saturday an emergency session, in which it voted on a bundle of decisions, including the rejection of the MoUs inked between the Government of National Accord (GNA) and Turkey.