In Tweets posted today morning, Division 13 said it had failed to push back an attack by al-Qaeda's Syrian affiliate, Al-Nusra Front, and allied faction Jund al-Aqsa.
Division 13 said the jihadists "raided all our bases and looted our weapons and equipment" in the town of Maarat al-Numan in Idlib province.
"We congratulate (Al-Nusra chief Mohammad) al-Jolani on this conquest!" the group posted sarcastically on Twitter.
According to the Syrian Observatory for Human Rights monitoring group, the clashes left at least six combatants dead, four of them identified as Division 13 fighters.
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He said the jihadists had cleared out Division 13's depots in Maarat al-Numan and three nearby towns, seizing US-made anti-tank TOW missiles.
A rebel alliance headed by Al-Nusra and Islamist faction Ahrar al-Sham captured full control of Idlib province last year.
Al-Nusra has previously attacked other factions who have received support from the United States. In the summer of 2015, it kidnapped several members of US-trained rebel group Division 30.
In recent weeks, tensions between Al-Nusra on one side and non-jihadist groups and activists on the other have boiled over.
Four days earlier, the group threatened to fire on anti-government demonstrators in Idlib city.