Turkish President Recep Tayyip Erdogan accuses the SDF of being allied to the Kurdistan Worker's Party (PKK), a US-designated terror group said to have carried out a November 13 bombing in Istanbul that killed six, including two children.
The PKK and SDF have denied playing a role in the Istanbul attack.
“We urged them [the Russians] to stop the Turkish attacks,” said Mr Abdi on Tuesday.
“The Turks insist on launching an operation on the ground. They are preparing for it … for us, it will be a battle for our existence.”
Mr Abdi called on foreign powers to respect a 2019 Russian-brokered agreement in which Syrian government forces were deployed along the northern border in exchange for Turkey halting an earlier offensive.
He has also called on the US to take a tougher stance on a threatened Turkish ground offensive.
The SDF commander earlier told Reuters he had received “clear” assurances from Washington and Moscow that they opposed a Turkish ground invasion but wanted something more tangible to hold back Ankara.
“We are still nervous. We need stronger, more solid statements to stop Turkey,” he said. “Turkey has announced its intent and is now feeling things out. The beginning of an invasion will depend on how it analyses the positions of other countries.”
Turkey has spent much of this year warning that a new offensive against the Kurds in Syria is imminent. The US-backed SDF gained control of parts of the country along the borders of Turkey and Iraq after defeating ISIS in a series of battles between 2014 and 2019.
But the US presence ― in some cases alongside Kurdish forces — remains small, with about 900 soldiers stationed mainly in eastern Syria.
The US has defended its position among the Kurds from ISIS, who are now on the wane, and groups loyal to Damascus, destroying a large force of Syria-backed mercenaries in February 2018.
But Turkey has the largest land army in Europe and the third largest air force in Nato. The US has been wary of a new offensive after three previous offensives left their forces dangerously exposed to Turkish air strikes.
Tension between Washington and Ankara has remained high, while the SDF, which has no air power, has reached out to both Moscow and the regime of Syrian President Bashar Al Assad to discuss ways to halt a new Turkish invasion.
Kurdish forces in the past have co-ordinated with Mr Al Assad’s troops, taking part in an offensive against Al Qaeda-linked forces in Aleppo in 2016.
But Mr Abdi told Reuters the SDF would not rely on Syrian air defences if Turkey launches a ground operation.
“Their position is weak compared to the Turkish army,” he said.
After years of international criticism for heavily bombing civilian areas, Russia has framed its work in Syria as a peace-building effort. Recent events have bought the SDF and Russia closer, in line with Mr Al Assad's goal of expelling Turkish forces from Syrian soil.
On Monday, Russia’s peace negotiations envoy for Syria, Alexander Lavrentiev, told the Moscow-linked Tass news agency that his country's aim was to stop further violence between Turkish forces — who already occupy belts of land in northern Syria alongside allied Islamist militias — and the Kurds.
“We are doing everything possible to ensure that violence should not come from those territories where Syrian troops are stationed and from the border zone,” he said.
In February 2020, Russian forces were forced to stand on the sidelines when Turkey accused Moscow’s Syrian allies of shelling Turkish troops, killing 33 soldiers. Turkey launched a major air offensive against Syrian forces, destroying dozens of tanks and armoured vehicles.