Sixteen Libyan soldiers were killed and 38 wounded in clashes around an eastern Islamist stronghold and close to a key oil terminal, military officials said Tuesday.
"The army lost 11 soldiers... in violent clashes with radical Islamists after an army offensive launched on Monday" near the town of Derna, said Colonel Ahmed al-Mashari.
He said the Islamist fighters had suffered "heavy losses" in the skirmishes.
The jihadist Islamic State (IS) group that has seized chunks of Iraq and Syria is thought to have gained a foothold in Derna amid the chaos in Libya since the 2011 uprising that ousted dictator Muammar Gaddafi.
Meanwhile, the Islamist-backed Fajr Dawn militia launched an offensive against troops loyal to Libya's internationally recognised government around the key oil hub of Al-Sidra, a military spokesman said.
Five soldiers died in the violence and another 13 were wounded, Colonel Ali al-Hassi said.
Oil is Libya's main natural resource, with a pre-revolt output capacity of about 1.6 million barrels per day (bpd), accounting for more than 95 percent of exports and 75 percent of the budget.
But production fell to about 350,000 bpd in December as an alliance of Islamist-led militias launched a bloody offensive to seize control of key terminals in the country's so-called "oil crescent".
More than three years after Gaddafi was toppled and killed in a NATO-backed revolt, the country remains awash with weapons and powerful militias, and has rival governments and parliaments.