By Ayman al-Warfalli

BENGHAZI, Libya (Reuters) - Libya's U.N.-backed unity government condemned an attack by a newly-formed militia group on eastern military forces close to key oil facilities, as clashes resumed on Sunday for a second day.

Fighting erupted south of the coastal town of Ajdabiya on Saturday between military units loyal to Libya's eastern government and a group calling itself the Benghazi Defence Forces. At least three people were killed and 10 wounded, military spokesman Akram Bu Haliqa said.

The Benghazi Defence Forces is largely composed of fighters pushed back earlier this year by brigades loyal to the eastern government commander Khalifa Haftar. Haftar has been waging a campaign for two years in Benghazi against Islamists, including some loyal to Islamic State, and other opponents.

The condemnation by the U.N.-backed Government of National Accord (GNA) is significant because some in the east suspect the GNA - whose leadership has itself been divided - of siding with Islamist-leaning militias.

The fighting near Ajdabiya, close to three oil terminals and north of major oil fields, risks opening a new front in the conflict between forces that backed competing governments set up in Tripoli and the east in 2014.

Since March, the GNA has been seeking to replace the rival parliaments and governments and integrate armed groups, including forces loyal to Haftar, into national security forces.

But the eastern parliament has held back from endorsing the new government, accusing it of legitimizing militias in western Libya whilst undermining the eastern military.

"The Presidential Council (of the GNA) strongly condemns this criminal act and holds the leaders and members of these militias fully responsible," said a statement published on the Presidential Council's Facebook page on Sunday.

"These militias are attacking to assist the remnants of the Islamic State terrorist organization in Benghazi and Ajdabiya which have faded and had their strength sapped by the strikes by our brave military."

Clashes erupted again early on Sunday, a resident said.

Armed groups in Libya have remained highly fragmented in the political turmoil that followed the toppling of Muammar Gaddafi in 2011.

Islamic State established a presence in several parts of the country from 2014, and has been active between Benghazi and the militants group's coastal stronghold of Sirte, about 380 km (240 miles) to the west.

In recent weeks, however, the ultra-hardline group has retreated into the center of Sirte after GNA-aligned forces advanced from the western city of Misrata.

The Petroleum Facilities Guard (PFG), a separate force that controls the oil terminals near Ajdabiya and is also aligned with the GNA, has pushed Islamic State back to the east of Sirte.

A PFG spokesman said the fresh outbreak of fighting did not immediately threaten oil facilities, but the PFG was ready to protect them if necessary.

(Additional reporting by Ahmed Elumami; Writing by Aidan Lewis; Editing by Ros Russell)