The development comes after the two leaders spoke on the phone on Sunday, Xinhua news agency reported.
In the call, the Presidents exchanged views on the safe zone agreed upon to be established in Syria, during which Erdogan complained to Trump on the US military and security "bureaucracy", said a statement released by the Turkish presidency.
Setting up a safe zone is essential for eliminating threat posed by outlawed Kurdistan Workers' Party (PKK) and the People's Protection Units (YPG), which Ankara sees as the Syrian branch of the PKK, and for facilitating the safe return of Syrian refugees to their country, Erdogan told Trump, according to the statement.
Turkey is determined to continue to fight the Islamic State (IS) in Syria and take all necessary measures to prevent such a problem in the region from happening again, Erdogan added.
On August 7, Turkish and US officials agreed to set up a safe zone and develop a "peace corridor" in northern Syria which would address Ankara's security concerns about the Kurdish faction that controls the territory.
The deal envisages withdrawal of the YPG towards the south of the safe zone. The safe zone would also facilitate the return of displaced Syr currently living in Turkey to their home country.
However, Ankara is dissatisfactory for delays in withdrawing the YPG group, while the US continues arms support to the Kurdish fighters. Turkey also wants to set up military bases in the planned safe zone.
Erdogan recently warned that Turkey can take unilateral military actions if the US fails to meet the requirements of the safe zone deal.
( With inputs from IANS )