At least 23 strikes were reported in several locations around the opposition-held northwestern province of Idlib, in what appeared to be the opening salvo of an expected offensive.
The head of the regime, Bashar al-Assad, has sworn to recapture every inch of Syria and has made big gains against the opposition since Russian Federation joined his war effort in 2015.
But Turkey, whose army has a string of observation posts around the edge of the rebel area, has warned against such an offensive.
Tuesday's strikes come after three weeks without Russian air raids in Idlib, though the Syrian military has kept up shelling and some aerial bombardment.
The situation around Idlib will be one of the main items on the agenda when the leaders of Russia, Iran and Turkey meet in Tehran this week, Peskov told reporters on a conference call, declining to elaborate further.
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Nearly two million people now in the area have already fled fighting in other parts of Syria.
US President Donald Trump on Monday warned the Syrian regime against launching an attack on Idlib, saying the offensive could trigger a "human tragedy".
Nikki Haley, the USA ambassador to the United Nations, wrote on Twitter late on Monday: "All eyes on the actions of Assad, Russia, and Iran in Idlib".
The UN has warned that an attack on Idlib, where 2.9 million people live, "will overwhelm capacities and has the potential to create a humanitarian emergency at a scale not yet seen through this crisis".
Since Russia's entry into the war on his side in 2015, Assad and his other close allies, Iran and a group of regional Shi'ite militias it backs, have forced the rebels from a succession of bastions including Aleppo, Eastern Ghouta and Deraa.
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Last week, Iran's defense minister traveled to Damascus and signed an agreement for defense cooperation between the two countries with his Syrian counterpart.
Located near the Turkish border, Idlib has been designated as a de-escalation zone where acts of aggression are expressly forbidden as part of the ongoing Astana process.
"By backing an all-out offensive, Russian Federation risks undermining its long-term political objectives in Syria", ICG wrote in a nine-page briefing.
Asked about the possibility of Israel hitting Iranian military positions in "Iraq or Tehran", Lieberman said: "We do not limit ourselves to Syrian territory alone".
Behind the scenes, American diplomats have been actively warning Moscow, which has been accused in the past of turning a blind eye to chemical weapon use by its Syrian proteges.
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While he quickly backed away from talk of an immediate withdrawal, his underlying determination to leave Syria's seven-year war as soon as possible seems unchanged.