"This deal may mark the start of a new approach but we still need more details," Aldar Khalil told AFP.
"We will evaluate the agreement based on details and facts, not headlines."
US State Department welcomes news of ceasefire in northwest Syria
Turkish and US officials agreed to establish a joint operations centre to oversee a safe zone to manage tensions between Ankara and US-backed Kurdish forces in Syria.
No details were provided of the size or nature of the safe zone, but the deal appeared to provide some breathing room after Turkey had threatened an imminent attack on the Kurdish People's Protection Units (YPG), which controls a large swathe of northern Syria.
The YPG has been a key US ally in the fight against the Islamic State group.
But Ankara views it as a "terrorist" offshoot of the Kurdistan Workers Party (PKK), which has fought a bloody insurgency inside Turkey for the past 35 years.
As the fight against IS winds down in northeastern Syria, the prospect of a US military withdrawal has stoked Kurdish fears of a long threatened Turkish attack.
Erdogan threatens operation against Syria Kurd militia 'very soon'
In recent weeks, Turkish media have repeatedly shown images of military convoys heading for the border area, carrying equipment and fighting units.
Khalil said Turkish President Recep Tayyip Erdogan was "still insisting on eliminating our presence," despite the deal with the US.
Turkey already carried out a cross-border offensive against the YPG in 2018, overrunning the majority Kurdish Afrin enclave in the northwest with the support of allied rebels.
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