A Kurdish political official familiar with the deal on Afrin said on Sunday that it was possible Russian Federation would object to the agreement as complicating its own diplomatic efforts with Turkey.
The aim of the operation is to establish security and stability along Turkey's borders as well as protect civilians from terrorists' havoc.
It was the first time the Syrian Democratic Forces (SDF), an alliance of Kurdish and Arab fighters, has claimed a cross-border attack on Turkish forces.
Although Syrian President Bashar al-Assad's government and the YPG have mostly avoided direct conflict, they have occasionally clashed and they espouse utterly different visions for Syria's future.
But negotiations have been ongoing for a potential return of government-affiliated forces to the enclave, officials have said.
Damascus has denounced Ankara's "aggression" but until Monday had not explicitly said it would intervene.
The military also said only terror targets were being destroyed and "utmost care" was being taken to not harm any civilian.
On Saturday, the head of Afrin hospital in northern Syria claimed that men were treated late Friday after shelling during the offensive and had symptoms that were in line with exposure to toxic agents. The Britain-based war monitoring group said medical sources in Afrin reported that six people in the attack suffered breathing difficulties and dilated pupils, indicating a suspected gas attack.
Ankara and allied Syrian rebels have waged a almost month-long offensive on Afrin, a northwestern pocket of Syria controlled by the Kurdish People's Protection Units (YPG), which make up the bulk of the SDF.
The move comes just days after Turkey was accused by the Kurds of hitting villages in Afrin in a chemical weapons attack. "(These are) lies. this is black propaganda". Turkey sees the YPG as terrorists and an extension of the banned PKK.
It has been listed as a terrorist organization by Turkey, the United States and the European Union. But while Washington has a military presence in the much larger swathes of Syria that the YPG and its allies control further east, it has not given support to the YPG in Afrin.