Turkish troops entered the Syrian territory in a sudden incursion which resulted in the occupation of Jarablus after Daesh left the city without resistance earlier this month.
Turkey has indicated that its eyes were now set on the Syrian city of Raqqah which is controlled by Daesh.
The senior Turkish official said on Friday a planned US offensive to retake Raqqah using Kurdish militia fighters would trigger an ethnic conflict there.
He said driving out Daesh from the Syrian city of al-Bab is also among the targets of Turkey's incursion into northern Syria.
On Sunday, Foreign Minister Mevlut Cavusoglu said Turkey was planning to send troops deeper into Syrian territory to establish what it calls a safe zone.
Damascus has condemned the incursion, denouncing it as a "flagrant breach" of its sovereignty.
Syria’s envoy to the UN Bashar Ja’afari said last week Turkey, along with the US and Israel, have moved from a proxy war to a “personal” one on the Arab state.
Turkey and Israel will mutually name ambassadors within 10 days as part of the normalization of ties, the Turkish official said.