The US-backed Syrian Democratic Forces has said it will co-ordinate with Syrian government troops to fend off any Turkish invasion of the north.
An SDF commander has said Damascus should use its air defence systems against Turkish planes.
Turkey has vowed a new offensive on parts of northern Syria controlled by the SDF, a Kurdish-led armed alliance that is led by the Kurdish People's Protection Units, or YPG.
The new threats have highlighted the complex web of ties in northern Syria.
Although Turkey considers the YPG a terrorist organisation, Syrian Kurdish forces are backed by Washington and have also co-ordinated with Syria's government and its ally Russia.
SDF head Mazloum Abdi said on Sunday that his forces were open to working with Syrian troops to fight off Turkey but said there was no need to send additional manpower.
"The essential thing that the Syrian army could do to defend Syrian territory would be use air defence systems against Turkish planes," Mr Abdi said.
'Crimes against humanity'
Syria regards Turkey as an occupying force in its north and the foreign ministry in Damascus said last month it would consider any new Turkish incursions as "war crimes and crimes against humanity".
Turkey has backed rebel groups in clashes against Syrian President Bashar Al Assad's forces and the SDF. It has used warplanes and drones to strike territory held by the SDF, where the Syrian-Kurdish authorities have set up an administration separate from Damascus.
Mr Abdi said more military co-ordination with Damascus would not threaten this autonomy.
"Our priority is defending Syrian territory, and no one should think about taking advantage of that situation to make gains on the ground," he said.
Turkish President Tayyip Erdogan has promised to capture the SDF-held towns of Tal Rifaat and Manbij in Syria's northern Aleppo province, most of which is otherwise held by Syrian government troops.
Turkish-backed incursions in previous years have ousted the SDF from the north-western enclave of Afrin and a series of border towns further east.
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Mr Abdi said a new offensive would displace about one million people and lead to wider zones of fighting, but would not confirm whether the SDF would respond with attacks inside Turkish territory.
He warned it could also lead to a resurgence of ISIS, which the SDF pushed out from territory in northern and eastern Syria with US air support.
SDF fighters guard camps and prisons where ISIS fighters and affiliated families are detained. Sending those guards to fight Turkey could leave security gaps.
"We cannot fight on two fronts," Mr Abdi said.
He said he hoped a coming meeting between the foreign ministers of Russia and Turkey could lead to de-escalation but said any negotiated settlement must include a halt to Turkish drone attacks in northern Syria.
"This would be one of our essential demands," he said.