The ceasefire grants the Kurdish-led forces, that were Washington's main Syrian ally in the fight against the Islamic State of Iraq and the Levant (ISIL or ISIS), five days to withdraw from the so-called "safe zone" Turkey wants to establish inside Syria.
Ankara launched a cross-border attack against Syria's Kurds on October 9 after the United States announced a military pullout from the north of the war-torn country, to widespread worldwide criticism. "If not, we will continue to crush the heads of the terrorists the minute the 120 hours (of the ceasefire) are over", Erdogan told flag-waving supporters in the central Turkish province of Kayseri.
"The immediate response based on self-defence was given", the ministry said.
Erdogan has said the Kurdish fighters must withdraw from a far larger length of the border from the Euphrates River to the Iraqi border - more than 440 kilometres (260 miles) - or else the Turkish offensive will resume on Tuesday. Erdogan said on Friday it would run for some 440 km from west to east along the border, though the United States special envoy for Syria said the accord covered a smaller area where Turkish forces and their Syrian rebel allies were fighting.
In Ras al-Ain, an AFP reporter saw at least 50 vehicles, including ambulances, leaving the town hospital, from which flames erupted shortly after their departure.
Redur Khalil, a senior Syrian Democratic Forces official, said the plan for evacuation from the town of Ras al-Ayn is set for today, if there were no delays.
Many said they were repulsed by Mr Trump's decision to host an worldwide summit at his own resort and incensed by acting White House chief of staff Mick Mulvaney's admission - later withdrawn - that U.S. aid to Ukraine was withheld for political reasons. The SDF has said the cease-fire was limited to the 120 km strip between the border towns of Tal Abyad and Ras al-Ayn.
A senior Syrian Kurdish official acknowledged for the first time that the Kurdish-led forces agreed to the pull-back, stating that his forces will move 30-kilometre (19 miles) south of the border.
A humanitarian worker, David Eubanks, with the Free Burma Rangers, speaking with CNN from northeastern Syria said they were also allowed to enter the town and were able to evacuate 37 injured people.
On Friday, Turkish-led bombardment killed 14 civilians in another part of the Kurdish-held region, according to the Observatory.
Vice President Mike Pence traveled to Turkey last week to negotiate a halt to the fighting as USA troops stationed in northeastern Syria prepared to withdraw.
The move has come under widespread criticism, even from within Trump´s own Republican party, notably because it opened the way for Russian Federation to further extend its influence in Syria. "We don't deal with the YPG, we deal with the Americans, so it's their responsibility", he said.
Turkey military operation in northern Syria has created a fresh wave of refugees.
A pull-back would be a major boost to the deal.
Abandoned by their American allies, the Kurds - with Russia's mediation - invited Damascus to send troops into northeastern Syria as protection from Turkish forces.
"It is in our interest that the American forces remain to maintain balance in Syria". Erdogan, who has backed rebels fighting to oust Assad, has said Turkey has no problem with Syrian government forces deploying near the border.