Mr Peskov said the al-Qaeda-linked jihadist fighters who dominate Idlib were threatening Russian military bases in Syria and blocking a political solution to the seven-year civil war.
Assad has vowed to defeat the opposition in its last refuge in the northwestern province if the rebels do not surrender to government rule.
"Hundreds of thousands of people could be killed".
Zarif met Assad to discuss "issues on the agenda for the tripartite meeting", according to the Syrian presidency's account on the Telegram messaging app.
An estimated three million people - half of them displaced from other parts of Syria - live in the province and adjacent rebel-held areas.
Assad's forces, backed by military support from Russian Federation and Iran, have recaptured major cities in recent years, often involving agreements with both opposition fighters and civilians that allowed them to flee to Idlib.
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According to opposition media sources, the Russian raids targeted dozens of sites in the countryside of Idlib and Al-Ghab plain, were concentrated in the areas of "Jisr al-Shughur, Jabal al-Zawiya, Mrouj, Al-Shagar, Harsh, Sinjul and more". Russia, like the Syrian government, refers to all opposition Syrian forces as terrorists.
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.
Tehran and Moscow have provided steady political, financial and military backing to Assad throughout the war, which has left over 350,000 people dead since it broke out in 2011.
A series of recent strikes in Syria that have killed Iranians has been attributed to Israel. The French Foreign Ministry is "ready to act" if Assad uses lethal chemical weapons, it said in a statement on Monday.
But analysts still say the United States appears resigned to the likelihood of a final military victory by Syrian regime forces.
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.
Trump has sought better relations with Russian Federation since taking office in 2017 but the United States has been unable to rein in Moscow's military and diplomatic support for Assad.