The accord on four zones was reached at Thursday's talks in Kazakhstan between Russia and Iran which back Syrian President Bashar al-Assad.
Turkey, which supports Syrian rebel groups, agreed to act as a guarantor. Moscow says the US, the UN and Saudi Arabia also support the idea.
But some delegates from the rebel forces angrily rejected the plan.
At Friday's news briefing in Moscow, Russian Deputy Defence Minister Alexander Fomin said attacks by all sides in the "de-escalation" zones should halt from midnight.