The zones appear meant to halt conflict in specific areas between government forces and rebels, and would potentially be policed by foreign troops.
Russian Deputy Defense Minister Lt. Gen. Alexander Fomin named Jordan as one of a number of countries already working with Russia in this effort.
And they include most of the Syrian government's military installations, such as the Shayrat air base, which the United States struck with missiles in retaliation for chemical attacks that killed scores of people in the rebel-held town of Khan Sheikhoun in Idlib province last month.
The call came as a Russia-initiated plan to set up safe zones was to take effect. There were no immediate reports of casualties. He did not elaborate on which those countries might be.
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The areas where coalition flights would be banned include Idlib province, where USA warplanes have been carrying out a series of airstrikes against what officials say are al-Qaida operatives.
A day after the United States gave tepid support for the establishment of Syrian safe zones to try to separate combatant forces and reduce the amount of fighting, they appear to have noticed that this might get in their way of their own attacks across the country, and are pledging to ignore the demilitarization of the zones.
Previous ceasefires have collapsed as Russian and Syrian jets continued to hit civilians under the premise of targetting hardline rebels.
The "de-escalation zones" will be closed to military aircraft from the USA -led coalition, the Russian official who signed the agreement, Alexander Lavrentye, said Friday.
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The country first announced plans to build the plane in 2008, but production issues repeatedly pushed the flight back. The industry ministry said in a statement the flight went smoothly and that all the systems functioned properly.
The guarantors will finalize maps of the de-escalation zones by June 4, and the agreement can be extended automatically if the three guarantor states agree. "Our operations are focused on ISIS, which are farther east".
Also, prospects for the success of the deal - agreed on by Russia, Turkey and Iran - are undermined by the failure of Syrian rebel groups who oppose President Bashar Assad to sign on to it. Turkey supports Syrian opposition forces.
Rebels, however, rejected the deal stating that Iran would not be recognised as a guarantor of any ceasefire.
Late Friday, a Syrian opposition coalition, the Higher Negotiating Committee, denounced the deal in a statement.
The Riyadh-based HNC, which includes political and armed groups, cautioned against attempts to "partition the country through vague meanings of what has been called".
A rebel commander confirmed that fighting had broken out after midnight, Reuters reports.
But the main Syrian opposition grouping says it has little faith in the deal.
Several ceasefires have been agreed since Syria's conflict broke out in March 2011, but they have failed to permanently stem the fighting.