The US has sanctioned two Turkish ministries and three senior government officials in response to the country’s military offensive in northern Syria.
President Donald Trump also phoned his Turkish counterpart Recep Tayyip Erdogan to demand an immediate truce, Vice-President Mike Pence said he would travel to the region “as quickly as possible”.
Syria’s army earlier entered areas in the north-east. This could result in a confrontation with Turkish-led forces.
The vice-president also reiterated that the US “did not give a green light to Turkey to invade Syria”.
Despite disagreeing with their attempts at self-rule, Mr Assad did not seek to retake the territory, especially after the Kurds became partners in the coalition against IS with US troops on the ground.
Apart from fighting IS, the Kurds were fundamental for the US in limiting the influence of rivals Russia and Iran and keeping some leverage on the ground.
For now, Syrian forces will not be deployed between Tal Abyad and Ras al-Ain, where Turkey has focused its efforts. Kurdish-led officials insisted they would remain in charge politically, and retain order in the area.
The Russian government, an ally of Mr Erdogan, said it did not want to entertain the possibility of a clash between Russian and Turkish forces in Syria, and said it was in regular contact with Turkey’s authorities.
Up to 160,000 civilians had been displaced, according to UN humanitarian agency OCHA, which said the number was expected to rise.
At least 50 civilians have been killed inside Syria and another 18 over the border in southern Turkey, reports say. Kurdish forces have confirmed the deaths of 56 of their fighters while Turkey says four of its soldiers and 16 pro-Turkish Syrian fighters have been killed in Syria.
Last week, US President Donald Trump abruptly pulled dozens of US troops from pockets in the north-east of Syria after a phone call with Mr Erdogan.
The move effectively paved the way for the operation by Turkey, which views elements of the Kurdish groups in Syria as an extension of the banned Kurdistan Workers’ Party, which has fought for Kurdish autonomy in Turkey for three decades.