"And it is not a coincidence that the United States has welcomed the result of the Astana meeting - an agreement to create de-escalation zones", Lavrov said.
Opposition activists in southern, central and northern Syria tell The Associated Press that there have been sporadic violations but the situation is by far much better than previous days with no airstrikes reported.
Sponsors of the deal hope safe zones will bring relief for hundreds of thousands of Syrian civilians and encourage refugees to return.
The chemical incident prompted the U.S.to fire dozens of cruise missiles at a Syrian airbase from which it said the attack had been launched, increasing tensions between the USA and Russian Federation. After past failures, this deal provides for the first time a mechanism to observe the cease-fire: Russian, Iranian and Turkish troops are to monitor compliance on the ground.
Government forces and rebels who have signed onto the deal will agree to halt all hostilities, including the use of warplanes, in the zones.
The memorandum came into force at 21:00 GMT on Friday.
According to the telegram, "the Turkish forces will temporarily deploy inside the border villages with armored vehicles and infantry forces as a first step" as the areas will be free of any presence of Syria or Russian warplanes.
The Britain-based Syrian Observatory for Human Rights and the Ghouta Media Center said a child was wounded in government shelling of the Damascus suburb of Kfar Batna.
The areas where coalition flights would be banned include Idlib province, where US warplanes have been carrying out a series of airstrikes against what officials say are al-Qaida operatives.
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On Thursday, as the agreement was being signed in Astana, the capital of Kazakhstan, some members of the Syrian opposition delegation shouted in protest and walked out of the conference room.
"In terms of their actions in the de-escalation zones then from this moment these zones are closed for their flights", the Kremlin's envoy to peace talks in Kazakhstan Alexander Lavrentiev was quoted as saying by Interfax news agency. Points to monitor the ceasefire will be also be arranged there, it indicated.
Asked earlier this year to comment on the idea of safe zones after it was raised by President Donald Trump, U.N. Secretary-General Antonio Guterres pointed to tragic examples such as Srebrenica, a U.N. -protected enclave in the Bosnian war where 8,000 Muslim men and boys were massacred in 1995.
"We can't imagine Iran playing a role of peace", Abo Zayd said.
The largest de-escalation zone includes Idlib province and adjoining districts of Hama, Aleppo and Latakia provinces.
On Wednesday, Syria's Foreign Ministry announced the acceptance of the Syrian government to the safe zone plan.
Ten days after signing the memorandum, the guarantor states will establish a joint working group, in particular for designating the borders of deescalation zones, according to TASS.
Syria has been locked in a vicious civil war since March 2011.
Captain Jeff Davis of the Pentagon would not say if the U.S. military would honour the zones and promise not to fly over them.