In Jordan and Turkey, Mr Jeffrey and Mr Rayburn will also focus on Syria and "reiterate the U.S. position that a military offensive in Idlib will escalate the crisis in Syria and the region, risk the lives of humanitarians and Syrian civilians, and destroy civilian infrastructure", the State Department said.
Russia, Assad's main military backer, has warned rebels may stage a chemical weapons attack and blame it on the regime in order to provoke a Western intervention.
U.N. High Commissioner for Refugees Filippo Grandi, speaking in Lebanon after a visit to Damascus, said he had appealed to both sides in the conflict "to try to find a solution, a way forward" that spares civilians.
Over the past few years, the regime, backed by Russian air power and Iranian-supported Shiite mercenaries on the ground, has retaken from the rebels Aleppo, Eastern Ghouta on the outskirts of the capital, and, most recently, Deraa Province-the origin of the 2011 uprising-along with the Golan Heights region bordering Israel.
But Lavrov on Wednesday called on the West not to stand in the way of what he described as an "anti-terror operation" in Idlib, which borders Turkey.
They include tens of thousands of rebels and civilians evacuated to Idlib from other areas recaptured by government troops.
The US Defense Department told Sputnik Thursday that it was aware of reports of a huge military exercise Russian Federation planned to stage in the Mediterranean Sea this week, and hoped Moscow would follow the rules of safe conduct.
"Attacking the whole of Idlib to eliminate some radical groups would mean causing the death of hundreds of thousands of people and making 3.5 million people leave their homes one more time", Cavusoglu added.
A major offensive in the Idlib area, where displaced people already make up half the population, risks forcing another 700,000 Syrians from their homes, the United Nations has said.
A total of 391 civilians, including 66 children, were killed in war-torn Syria last month, according to a Syrian NGO on Saturday. Russian Federation has said a military operation there is necessary to weed out "terrorists" it blames for attacking its bases on the coast. The province contains an array of militant groups, including the ultra-radical Levant Liberation Committee (LLC), which is also known as the al-Qaida-linked Nusra Front. HTS is now the most powerful armed faction in Idlib.
Turkey has 12 military observation posts inside Idlib aimed at monitoring a de-escalation zone and media reports have said it has sent concrete blocks over the border to reinforce them in case of an assault. On Friday, however, Turkey officially declared the group a terrorist movement, a designation also used for the group by the United States and European Union.
President Recep Tayyip Erdogan will travel to Iran to meet with his Russian and Iranian counterparts Vladimir Putin and Hassan Rouhani, state-run TRT Haber television said.
The campaign for Idlib is likely to be the last major theater of battle after seven years of brutal civil war.