Details about the borders of the zones and which of the guarantor countries would be responsible for securing each one, were vague.
A spokesman for the Iranian Foreign Ministry, Bahram Qasemi, confirmed on Monday that the troop movement, made on Sunday, was within the framework of the Astana accord.
But rebels fighting militants ISIS for its de facto capital of Raqqa criticized the recent moves by Turkey.
Ahmed al-Sultan, deputy commander of the Jaish Al-Thowar, a main faction of the US-backed Syrian Democratic Forces coalition, claimed the Turkish move was an attempt to stop the Kurdish-dominated force from advancing towards Idlib once the battle in Raqqa is complete.
He claimed Turkey was trying to cut off the Kurdish-dominated Syrian city of Erfin and prevent Kurdish rebels from expanding the areas under its control. He also dismissed Turkish claims of fighting terrorism in Idlib, accusing Turkey of instead coordinating with and supporting the al-Qaeda splinter groups.
Turkey backs anti-extremist drive
Erdogan justified his moves as necessary "precautions," saying during a party address in Afyonkarahisar on Sunday that the border provinces are "under threat."
"If we do not take precautions, today three, five, 10, 20 mortars are falling into Turkey, tomorrow there may be bombs. When we respond to them within the rules of engagement, they quiet down," Erdogan said. "We are realizing the strategy that we planned."
Idlib is the last remaining area in northern Syria where anti-Assad rebel groups have a foothold. But the FSA has increasingly lost territory to extremist Islamist groups there.
In recent months, the province has fallen under the control of Hayat Tahrir al-Sham (HTS), the latest reincarnation of the formerly al Qaeda-affiliated al Nusra Front. FSA and HTS oppose the Assad regime, but are also battling each another for control of the province.
Following news of the Turkish-backed operation, HTS issued a statement on its Telegram channel warning FSA units against participating.
"If you want to die, orphan your children...step your feet into Idlib. The news is what you see, not what you hear," HTS said.
Rebels unwilling to accept Russian participation
Russia is joining with Turkey in providing security in Idlib, Erdogan said Saturday, without elaborating further. But FSA groups have denounced any Russian involvement, which they accuse of supporting the Assad regime through bombings in...
Read More: Turkish forces scout Syria's Idlib province