"I was part of a phone call yesterday between President Erdogan and President Trump where President Trump received a commitment from the President of Turkey to stay away from the Kobani area to prevent further escalation in Syria," US Senator Lindsey Graham - one of the main supporters of the US president in the Senate - said on Twitter, Efe news reported.
"If Turkey continues to move and take Kurdish areas around Kobani, I will take this as a breach of President Erdogan's promise and a major escalation," the Republican lawmaker said.
"I am certain Congress and the Administration will hold Erdogan personally responsible for any atrocities committed in and around Kobani," he added. "My advice to Turkey is stop before you completely destroy the relationship between the United States and Turkey."
US Vice President Mike Pence and Secretary of State Mike Pompeo will travel to Ankara in the next 24 hours to negotiate a ceasefire that will end Turkey's military operations against the Kurds in the north of Syria, Trump announced Tuesday.
A senior US official declined to detail in statements to journalists if Pence would meet with Erdogan and simply said that the purpose of the trip was to negotiate a ceasefire and show the Turkish government that the US was upset with its offensive in northern Syria.
The Turkish offensive, which began October 9, is directed against the Kurdish People's Protection Units (YPG) that Turkey considers terrorists, but are allies of Washington in the fight against the Islamic State terror group.
Trump already demanded Erdogan on Monday declare a ceasefire during a telephone conversation.
On Monday, in another call, the US president also informed his objective to the commander of the Syrian Democratic Forces, Mazlum Abdi, whose organization brings together the YPG and other armed groups, said the official.
Erdogan said Monday that he would continue with his plans to take control of a strip of territory across northeastern Syria, despite the announcement that the government of Syrian President Bashar al-Assad has sent troops to curb the offensive.
The Turkish president assured that he had spoken with the Russian executive and that he had given his approval to expand the offensive towards Kobani and the Manbech region.
"It looks like Turkey's operation won't have any problems in Syria's Ayn al-Arab as Russia also showed a positive approach," Erdogan said.
( With inputs from IANS )