Pope Francis appealed for peace and dialogue as the Syrian government and its allies prepare to launch strikes against the last major rebel stronghold in Idlib province in the country's northwest. The Observatory said 13 people were killed.
The province bordering Turkey is home to almost three million people, up to half of whom are rebels and civilians transferred en masse after pro-government forces retook formerly rebel-held areas.
"Syria's territorial integrity should be safeguarded and all tribes and groups, as one society, should start the reconstruction process, and the refugees should return to their homes", Zarif said, according to Iran's Fars news agency.
Mr Pompeo retweeted the United States president's remarks about Idlib.
The U.N.'s special envoy to Syria, Staffan De Mistura, urged Russian Federation and Turkey to reach a "soft solution" to avert an expected government offensive on the province.
Assad and Zarif said Western pressure on Tehran and Damascus will fail to deter them from fighting terrorism.
Behind the scenes, American diplomats have also been actively warning Moscow, which has been accused in the past of turning a blind eye to chemical weapon use by its Syrian proteges.
Damascus's main sponsor Russian Federation has been sounding the war drums in recent days, all the while seeking to pressure Turkey into reining in jihadists in Idlib.
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Russian, Turkish and Iranian leaders are due to meet on Friday in Iran to discuss the situation in northwestern Syria. De Mistura said he heard from media reports that a campaign for Idlib could begin as early as the following Monday.
He called for humanitarian corridors to be set up to allow civilians to be evacuated temporarily.
Idlib and the surrounding area is home to some 3 million people - almost half of them already displaced a few times by the civil war - choosing to live in opposition areas.
Regime ally Moscow and rebel backer Ankara have held several rounds of talks aimed at averting an assault, but government troops have been massing near the rebel zone.
They are home to some three million civilians.
Separately, the White House warned that the USA and its allies would "respond swiftly and appropriately" against the Syrian government if it uses chemical weapons in its assault. Zarif did not say whether the meeting will take place between the presidents of the three countries or between other senior officials.
U.S. President Donald Trump warned Assad and his allies on Monday not to "recklessly attack" Idlib, saying hundreds of thousands of people could be killed.
Last week the United Nations envoy to Syria, Staffan de Mistura, said the Nusra Front and al Qaeda, both of which the worldwide body designates as terrorists, had an estimated 10,000 fighters in Idlib.
"Just to speak out with some warnings, without taking into account the very risky, negative potential for the whole situation in Syria, is probably not a full, comprehensive approach", Kremlin spokesman Dmitry Peskov said, apparently in reference to Trump's comment.