The Syrian Kurdish YPG militia said on Thursday that fighters backing the Syrian government were deploying on the frontlines to help repel a Turkish assault, but that assistance would be needed from the Syrian army itself.
In a sign of a possible concession to Damascus, the YPG said later on Thursday that it had quit districts it held in north Aleppo, which were then taken by the government.
"Groups aligned to the Syrian army came to Afrin, but not in the quantity or capacity to stop the Turkish occupation," YPG spokesman Nouri Mahmoud told Reuters. "The Syrian army must fulfil its duty ... to protect Syria's borders."
Pro-Damascus militias arrived in the northwesterly Afrin region late on Tuesday in response to a request by the YPG to Syrian President Bashar al-Assad's government.
Hundreds of those fighters have deployed on front lines in Afrin battling Turkish forces, Mahmoud said.
But Assad did not send the army itself, a move that could have sparked a wider direct confrontation with Turkey.
Ankara, a pro-Assad commander and Kurdish officials have all said recently that Russia intervened to stop Damascus sending the army to defend Afrin after reports of a deal with the Syrian Kurdish forces.
While Russia is Assad's strongest ally in the war, it is also working with Turkey, which backs rebel factions, to negotiate a wider settlement to the conflict.
On Thursday, Turkish Deputy Prime Minister Bekir Bozdag said he believed there was no deal in place between the Syrian government and the YPG.
"We have information that they have not reached a deal," Bozdag said in a televised interview.
However, the YPG commander of a Kurdish-held enclave in Aleppo said the government had regained control over districts there after the militia pulled out to help relieve Afrin.
Earlier on Thursday, a witness and a war monitoring group said government forces had moved into the enclave.
Assad has repeatedly said he wants to take back every inch of Syria, but the state had tolerated Kurdish control over the Kurdish-majority Sheikh Maqsoud area and nearby Aleppo neighbourhoods that the YPG captured from rebels in late 2016.
The government and the Kurdish forces control more of Syria than any other side in the war, and any signs of dealmaking between them are closely watched.
Both Assad and the YPG regard Turkey as an enemy. Ankara was one of the biggest powers supporting anti-Assad rebels early in the war, and is now targeting the Kurdish militia, which it sees as an offshoot of the PKK insurgency it is fighting at home.
Turkey launched its air and ground offensive on Afrin last month, seeking to drive out the YPG, which it deems a security threat along its border.