This comes as a summit is set to be held in the Iranian capital Tehran in the presence of the leaders of Russia, Turkey and Iran regarding Syria. United Nations officials warned this week of a humanitarian catastrophe if a military offensive in Idlib moves forward.
Tehran and Moscow have helped Assad turn the course of the war against an array of opponents ranging from Western-backed rebels to Islamist militants, while Turkey is a leading opposition supporter and has troops in the country. At least one person was killed and several others wounded.
The two men, shown arriving by plane by Iranian state television, were due to hold talks with Iranian President Hassan Rohani.
There are tens of thousands of rebels in Idlib Province, which borders Turkey.
On Monday, President Trump joined a growing chorus of voices warning the Syrian government against a full scale assault, which he said could trigger a "human tragedy". Jefrey said the goal is to produce a political solution in Syria that stops the fighting and prevents conditions for a return of ISIS or another extremist group.
As for Trump's take on the reversal, Jeffrey said, "I am confident the president is on board with this".
On Wednesday, Putin's spokesman Dmitry Peskov said Idlib was the "subject of increased concern and worry" and the focus of a flurry of diplomacy.
As sides close in on the remaining jihadist forces operating in Syria, Jeffrey said it was time for a "major diplomatic initiative" to end the seven-year conflict.
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Russian President Vladimir Putin however, said that he was against a ceasefire because Nusra Front and Islamic State of Iraq and the Levant (ISIL) fighters located there were not part of peace talks.
Meanwhile, the Russian Foreign Ministry said on Thursday that the country will continue to kill "terrorists" in Idlib and elsewhere in Syria to bring back peace. "God forbid, it is again Turkey where those people will flee in case of a disaster", Erdogan said.
"3.5 million people live there". Jeffrey said there will be a "major diplomatic initiative" to stabilize conditions in Syria in the coming weeks, but he would not describe the military mission, other than to say that they must ensure an "enduring defeat" of ISIS. "Turkey has filled its capacity to host refugees".
Widely abhorred internationality for the brutal conduct of the war, Assad has largely reclaimed most of Syrian territory though much of it is ravaged.
The final statement of the summit between Russia, Turkey and Iran has already been finalized by senior representatives from the countries, according to Hossein Jaberi Ansari, Iran's top negotiator in the discussions.
Meanwhile, the fate of Idlib hung in the balance.
"Let's try to avoid that the last probably major battle of the Syrian territorial conflict...ends in a bloodbath", he told reporters in Geneva, insisting Russian Federation and Turkey held "the key for the soft solution to the Idlib issue".
"It will be waged irrespective of civilian casualties, even though they will make an effort to minimize it".