The dominant force in the northwestern region bordering Turkey, the Hayat Tahrir al Sham (HTS) alliance led by militants of Syria's former Al Qaeda affiliate, had on Sunday however still not responded.
Late Saturday, the National Liberation Front (NLF) militant alliance in a statement accepted the deal reached on Monday for Idlib, but said they remained on their guard.
Thousands head home in Syria's Idlib after deal: monitor
They announced "our full cooperation with our Turkish ally in helping to make a success their efforts to spare civilians from the afflictions of war".
"But we will stay alert to any betrayal by the Russians, the regime or the Iranians," the NLF warned, fearing the agreement to be 'temporary'.
"We will not abandon our weapons, our land or our revolution" against the Russia- and Iran-backed forces of President Bashar al Assad, the militants said.
Also on Saturday, in a statement circulated on social media, the Al Qaeda-linked Hurras al Deen rejected the agreement reached in the Russian resort of Sochi.
"We at the Hurras al Deen organisation again announce our rejection of these conspiracies," it said.
Monday's agreement provides for a U-shaped buffer zone 15 to 20 kilometres wide to be set up around Idlib.
Under the deal, all factions in the planned demilitarised zone must hand over their heavy weapons by October 10, and militant groups must withdraw by October 15.
Both the Hurras al Deen and NLF militants are present inside this planned buffer area, the Syrian Observatory for Human Rights says.
But the dominant HTS alliance is also widely present, according to the Britain-based monitor.
Russia discussing situation in Syria's Idlib with Iran and Turkey
The militant-led group--which controls more than half of the Idlib region--has not officially responded to the agreement.
But its propaganda agency Ebaa has cast doubt on Turkey's motivations.
In August, HTS leader Abu Mohamed al Jolani warned opposition factions in Idlib against handing over their weapons.
Syria's war has killed more than 360,000 people and displaced millions from their homes since erupting in 2011 with the brutal repression of anti-Assad protests.
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