Russia has not officially released its proposal, but reports in Russian state media said the zones would be patrolled by forces from Russia, Iran and Turkey.
In a telephone conversation Tuesday, the USA and Russian presidents agreed to bolster diplomatic efforts to end Syria's six-year-old civil war.
"Still some hopes, disappointment and caution", Vladimir Frolov, a prominent foreign policy analyst and columnist, said of the atmosphere in Moscow.
Instead the opposition said it was halting its participation as the fourth round of talks sponsored by Assad allies Russian Federation and Iran and rebel supporter Turkey began.
Some of the trade restrictions introduced after the Russian jet was shot down are still in place, a lingering irritation in Russian-Turkish relations. Turkey has repeatedly asked the USA and Russian Federation to cut their ties with the Syrian Kurdish YPG, which is fighting against the Islamic State of Iraq and the Levant (ISIL).
The Turkish leader said he hoped the concept of a "zone of de-escalation" would be accepted at the talks on Syria going on simultaneously in Astana, the Kazakh capital, with Iran and the U.S. also in attendance.
According to Russian-state media, plans for at least four "de-escalation zones" were being considered in Astana.
The document accuses Russian Federation of not fulfilling its role as a guarantor of the agreement.
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The safe zones would end violence and allow for the return of refugees and the delivery of aid. But Russia's ongoing support for Assad has been a persistent roadblock.
After the meeting - their second in as many months - Putin and Erdogan agreed formally to restore bilateral ties between their countries and restore trade and services that had been impacted by restrictions imposed by either side.
Economic ties between the two countries had always been on a positive track until, as Putin put it, Turkey "stabbed Russia in the back" by shooting down a Russian fighter jet over the Turkish-Syrian border in November 2015.
"It is also planned to consider current regional and global problems, first of all those related to fighting against terrorism and the settlement of the Syrian crisis".
According to Bibilov's administration, he also inquired into the possibility of Soviet era savings deposit reimbursements to South Ossetians, as well as "the abolition of Value-Added Tax on goods produced in South Ossetia and imported into the Russian Federation".
The Britain-based Syrian Observatory for Human Rights says the death toll in the town of Azaz is likely to climb after Wednesday's blast.
"In particular, departmental consultations on anti-terrorist operations will continue to be held on a regular basis". The Observatory and the activist-run Azaz Media Center confirmed the toll, which was likely to rise.