* Old parliament reconvened after appeal from fighters
* New legislature had been intended to help country progress
* Egypt, UAE carried out air strikes, U.S. officials say (Adds report of Egypt, UAE involvement in air strikes, joint statement)
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 the new prime minister, leaving the chaotic country with two rival leaders and assemblies, each backed by armed factions.
As political unrest mounted, U.S. officials said two series of air strikes in the past week on armed Islamist factions in the capital, Tripoli, were the work of Egypt and the United Arab Emirates.
The officials said the two countries, both of which have cracked down on Islamists, used aircraft based in Egypt and acted without consulting Washington. The details were first reported by the New York Times.
Egypt has denied conducting air strikes or other military operations in Libya.
At a meeting of Libya's neighbours on Monday in Cairo, Libya appealed for international protection of its oilfields and airports, saying it lacked the power to stop armed groups.
An election in June had been aimed at rebuilding state institutions in an attempt to quell three years of spreading violence since the ouster of long-time ruler Muammar Gaddafi.
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 weapons on each other to achieve a power monopoly 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 Tripoli, appointed Omar al-Hasi, spokesman Omar Hmeidan said.
Hasi had tried to become prime minister in April with the backing of Islamists and independents in the old parliament.
The House of Representatives meets in the eastern town of Tobruk, far from the clashes in Tripoli and Benghazi.
"The House of Representatives is the only legitimate body in Libya," Prime Minister Abdullah al-Thinni told a televised news conference, condemning as invalid the GNC decision to appoint a new prime minister.
CALL FOR HELP
In a call for foreign assistance, Libya's ambassador to Egypt, Mohamed Jibril, said on the sidelines of the Cairo meeting: "There are forms of international intervention (possible) particularly since Libya is unable to protect its institutions, its airports and natural resources, especially the oilfields."
But in a lacklustre response, Libya's neighbours agreed not to intervene in domestic affairs, calling instead for a national dialogue - an approach already tried by the United Nations, without success.
Over the weekend, Tripoli residents said unidentified war planes attacked targets there. Also, there were strikes on Islamist-held positions last Monday.
The New York Times quoted U.S. officials as saying Egypt had provided launching bases for the strikes, while the pilots, warplanes and aerial refuelling planes were from the UAE.
Libya's ambassador to the United Nations, Ibrahim Dabbashi, was sceptical about Egypt and UAE involvement, telling Reuters: "I don't believe it."
"They are not even technically capable, and it would also be a very sensitive thing for them politically," he said. He declined to speculate on who else might have been behind the air strikes.
U.S. State Department spokeswoman Jen Psaki refused to address the report when asked about it on Monday at a regular department briefing in Washington.
But in a joint statement, the United States and major European allies cautioned that "outside interference in Libya exacerbates current divisions and undermines Libya's democratic transition."
They repeated calls "that all parties in Libya accept an immediate ceasefire and engage constructively in the democratic process."
Western powers fear that Libya will turn into a failed state or a civil war will erupt as the government is unable to control various armed groups in a country awash with heavy weapons.
Also on Monday, unknown attackers used a Grad multiple rocket launcher to attack Labraq airport, said its director, Abu Bakr al-Abidi. The airport was still operating.
Labraq, east of Benghazi, has become a major gateway into Libya since Egypt and Tunisia last week cancelled nearly all flights to Tripoli and the west of the country, citing security reasons.
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; Mark Hosenball in Washington and Louis Charbonneau at the United Nations; Editing by Alison Williams, Peter Cooney and Gunna Dickson)