The ceasefire will last six months and could be "automatically extended" for another six months, Alexander Lavrentyev said Friday after talks in Astana, Kazakhstan.
Turkey's state-run Anadolu news agency also reported on the ceasefire -- signed by Russia, Turkey and Iran -- saying a joint working group will be set up by the agreement's three guarantor countries to determine the precise borders of the four zones by June 4.
The security zones would be in place in Idlib province, to the north of the city of Homs, in Eastern Ghouta near Damascus, and in southern Syria.
Such zones, also referred to as non-conflict or safe zones, are meant to be areas where civilians can live without being targeted by any party in Syria's war. However, key issues would involve whether and how the zones would be enforced.
The High Negotiations Committee, a Syrian opposition group, said the agreement is not legitimate because the UN Security Council is the party delegated to oversee all negotiations on the country's brutal six-year conflict. The group also criticized Syrian President Bashar al-Assad, saying he was trying to partition the nation into useful and non-useful regions.
Russia and Iran are both key backers of Assad. Turkey supports Syrian opposition forces.
Russian Foreign Minister Sergey Lavrov and US Secretary of State Rex Tillerson shared a phone call Friday discussing the zones, the Russian foreign ministry said, according to Russian state media news outlet TASS.
"The focus was made on the topic of the Syrian settlement," the ministry said, according to TASS.
A State Department official who didn't want to be identified told CNN, "The United States supports any effort that can genuinely de-escalate the violence in Syria, ensure unhindered humanitarian access, focus energies on the defeat of ISIS and other terrorists, and create the conditions for a credible political resolution of the conflict.
A spokeswoman for US President Donald Trump commented on the safe zones at the White House daily media briefing.
"The President's expressed a desire to achieve peace in Syria ... and we're looking at all ways in order to achieve that," deputy press secretary Sarah Huckabee Sanders said. "And we haven't laid out any specifics any further than that at this point."
There were reports that the safe zones would be no-fly areas for warplanes from the US-led coalition.
"The coalition will continue to strike ISIS targets in Syria. The campaign to defeat ISIS will continue at the same relentless pace it is proceeding now," the State Department official told CNN.
Earlier, a Pentagon spokesman, US Navy Capt. Jeff Davis, referred CNN to the State Department for comment but said the de-escalation zones are west of where ISIS operates in Syria.
TASS reported Thursday that Moscow says no warplanes will fly over the four safe zones.
"We express the confidence that after such a statement, the flights by Syrian combat aircraft and their operation on the territory of de-escalation zones will cease," Lavrentyev said, according to TASS.
Syria's Foreign Ministry said Wednesday it accepted a Russian proposal to create de-escalation zones, vowing not to shell the areas in compliance with a largely ignored ceasefire agreed to in December.
The Foreign Ministry said regime forces would continue fighting terrorists from ISIS and al Qaeda's former affiliate in Syria, al Nusra Front, according to a statement carried by the state-run Syrian Arab News Agency.