The military aircraft came down in Al-Baida in eastern Libya after carrying out air strikes targeting Islamists in Derna farther east, a spokesman for general Khalifa Haftar said.
Speaking on condition of anonymity, he said the crash happened because of a "technical" glitch, and added that the pilot was killed.
But the Ansar al-Sharia jihadist group, which Washington classifies as a "terrorist organisation" said on social networks that its militants fired a missile at the plane.
Haftar in May launched an offensive dubbed "Operation Dignity" against radical Islamists in Benghazi, Libya's second city and birthplace of the 2011 uprising that toppled dictator Moamer Kadhafi.
Also Read
Ansar al-Sharia is based in Benghazi and is said to control 80 percent of the city.
Libya has been sliding into chaos since Kadhafi was overthrown and killed three years ago, as the embattled interim authorities confront powerful militias who fought to oust the veteran dictator.
Last weekend, the Fajr Libya (Libya Dawn) mainly Islamist alliance seized Tripoli airport after weeks of fierce fighting with nationalist rivals.
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 alarm 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 Islamist positions near Tripoli airport.
Egypt, the UAE and oil kingpin Saudi Arabia view Islamist militants in the region as a serious threat and have cooperated against what they see as a common danger.