* Old parliament reconvened after appeal from fighters
* New legislature had been intended to help country progress
* Neighbours decline call for help, instead urge dialogue (Recasts with old parliament reconvening, Egypt meeting)
By Feras Bosalum and Ulf Laessing
BENGHAZI, Libya/CAIRO, Aug 25 (Reuters) - The Libyan parliament that was replaced in an election in June reconvened on Monday and chose an Islamist-backed deputy as prime minister, leaving the chaotic country with two rival leaders and assemblies each backed by armed factions.
The election was meant draw a line under another incidence of competing prime ministers in May and allow nation building to being to try to quell three years of spreading violence since veteran ruler Muammar Gaddafi was ousted.
But the old General National Congress (GNC), where Islamists had a strong voice, has refused to acknowledge the legitimacy of its successor assembly, the House of Representatives, which is dominated by liberals and federalists.
The GNC reconvened after armed factions from the western city of Misrata forced a rival faction from Zintan out of Tripoli's main airport on Saturday after a month of fighting that has come to symbolise the country's deep divisions.
The Zintanis and Misratis joined forces in 2011 to topple Gaddafi but have now turned their guns on each other to monopolise power and exploit Libya's oil resources.
The Misrata-led brigade, backed by an Islamist militia called Operation Dawn, had called on the GNC to resume work. Many in Misrata feel the new parliament does not represent the majority. The Zintan faction opposed the old assembly.
The GNC, which met in the capital Tripoli, elected Omar al-Hasi as its new leader, spokesman Omar Hmeidan said.
Hasi had tried to become prime minister in April with the backing Islamists and independents in the old parliament.
The House of Representatives meets in the eastern town of Tobruk, far from the continuing clashes in Tripoli and Benghazi.
Libya earlier appealed to the international community to help protect its oilfields, airports and other state assets as it is too weak to stop armed groups.
"There are forms of international intervention (possible) particularly since Libya is unable to protect its institutions, its airports and natural resources, especially the oilfields," Ambassador Mohamed Jibril said on the sidelines of a meeting of Libya's neighbours in Cairo.
But in a lacklustre response, Libya's neighbours agreed not to intervene in domestic affairs, calling for a national dialogue instead - an approach already tried by the United Nations with no success.
Libya's appeal for foreign aid came as unknown attackers used a Grad multiple rocket launcher to attack Labraq airport, its director Abu Bakr al-Abidi said. The airport was still operating.
Labraq, east of Benghazi, has become a major gateway into Libya since Egypt and Tunisia cancelled almost all flights to the capital Tripoli and the west of the country last week, citing security reasons.
Tunis Air suspended flights to Labraq and Tobruk on Sunday, Libyan officials said. It was one of the last foreign airlines still flying to Libya after rival factions turned Tripoli International Airport into a battlefield last month.
Benghazi's own airport has been closed since May when a renegade general launched a military campaign on Islamists in the port city. (Additional reporting by Ahmed Elumami and Heba al-Shibani; Editing by Alison Williams)