Libyan fighters have said that they downed a plane belonging to militia forces of General Khalifa Haftar, but a source close to the officer said it crashed because of a technical fault.
The military aircraft came down in al-Baida in eastern Libya on Friday after carrying out air strikes targeting armed groups in Derna farther east, a spokesman for general Haftar said.
Speaking on condition of anonymity, he said the crash happened because of a "technical" glitch, and added that the pilot was killed.
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But the Ansar al-Sharia rebel group, which the United States classifies as a "terrorist organisation" said on social media that its fighters fired a missile at the plane.
Neither claim could be independently confirmed.
Haftar in May launched an offensive dubbed "Operation Dignity" against rebel fighters in Benghazi, Libya's second city and birthplace of the 2011 uprising that toppled Muammar Gaddafi.
Ansar al-Sharia is based in Benghazi and is said to control at least 80 percent of the city.
Libya has been sliding into chaos since Gaddafi was overthrown and killed three years ago, as the embattled interim authorities confront powerful militias who fought to oust the former leader.
Last weekend, the Fajr Libya (Libya Dawn) alliance seized Tripoli airport after weeks of fierce fighting with nationalist rivals.
And the crisis has further deepened with factions backing rival prime ministers and rival parliaments.
On Wednesday, the 15-member UN Security Council unanimously adopted a resolution for an immediate ceasefire in the oil-rich North African country and tightened an arms embargo.
The council also moved to impose sanctions on the militias and their political supporters, amid mounting fears that full-blown civil war could erupt in Libya.
But in a show of defiance, several thousand Libyans rallied Friday in Tripoli in support of Fajr Libya.
The protesters also torched the flags of Egypt and the United Arab Emirates, two countries which the US says carried out air strikes this month on rebel positions near Tripoli airport.
Egypt has denied any "direct" role in the air strikes while the UAE has kept silent.
Egypt, the UAE and oil kingpin Saudi Arabia view fighters in the region as a serious threat and have cooperated against what they see as a common danger.