By Ayman al-Warfalli

BENGHAZI, Libya (Reuters) - Forces loyal to Libya's eastern leadership launched attacks near the town of Ajdabiya on Tuesday against a newly formed rival brigade, in fighting that threatens to prolong the country's conflict and expose divisions in a U.N.-backed unity government.

Libya has been blighted by a power vacuum over the past two years, in which loose alliances of armed groups aligned with rival parliaments and governments in Tripoli and the east have fought for supremacy.

On one side of the most recent air and ground battle are Libyan National Army (LNA) units loyal to eastern commander Khalifa Haftar, who has been waging a campaign against Islamists and other opponents in Benghazi since 2014.

On the other are several hundred men from the recently named Benghazi Defense Forces (BDF), which says it wants to take back control of Libya's second city. They include members of the al Qaeda-linked militant group Ansar al Sharia.

Ajdabiya is situated about 150 km (93 miles) south of Benghazi, close to major oil terminals and fields and the site of power and water facilities.

The BDF attacked Haftar's forces on the southern outskirts of Ajdabiya on Saturday, claiming to have taken control of several LNA positions. On Monday and Tuesday, LNA war planes retaliated with strikes near a flour mill south of the town, military officials said.

A medical source said a number of civilians in Ajdabiya had been wounded by mortar fire, some seriously.

A separate force that controls the oil terminals, the Petroleum Facilities Guard (PFG), said on Monday that an LNA strike had hit a PFG training camp, causing damage. A spokesman for the Guard, Ali al-Hassi, promised a "harsh response".

The PFG used to be allied to the eastern military but has now switched its allegiance to the U.N.-backed Government of National Accord (GNA).

The GNA was designed to replace Libya's two other competing administrations, and has been trying to assert its authority from the capital Tripoli, which lies hundreds of kilometers west of Benghazi, since March.

It has yet to win crucial backing from allies of Haftar in the eastern parliament.

The GNA's Presidency Council issued a statement on Sunday condemning the attack by the BDF, but at least one member of the Council later distanced himself from the statement. Two members of the Council associated with eastern factions have already suspended their membership.

The fighting in Ajdabiya comes as brigades aligned with the GNA are engaged in a campaign to recapture Islamic State's Libyan stronghold of Sirte, some 370 km to the west.

Brigades based in the city of Misrata have advanced to the edge of Sirte from the west, and the PFG has retaken coastal territory from the jihadist group to the east.

(Writing by Aidan Lewis; editing by John Stonestreet)