The Kurdish-led authorities in north-eastern Syria say a US-backed Kurdish militia has begun withdrawing from territory along the border with Turkey.
The "first practical steps" came on the weekend, when the People's Protection Units (YPG) pulled out some fighters and weaponry from two areas.
The move is part of a deal with Turkey and the US, which has forces there.
Turkey has threatened to launch an assault unless the YPG pulls back from the border and a "safe zone" is set up.
It considers the YPG a terrorist group, saying that it is an extension of the banned Kurdistan Workers' Party (PKK), which has fought for Kurdish autonomy in Turkey for three decades.
The YPG played a leading role in the Syrian Democratic Forces (SDF) alliance that was the US military's main partner on the ground in Syria in the battle against the jihadist group Islamic State (IS).
On 7 August, US and Turkish military delegations agreed on "the rapid implementation of initial implementation of initial measures to address Turkey's security concerns" along its border with Syria, according to a statement from the US embassy in Ankara.
The delegations also said they would "stand up a joint operations centre in Turkey as soon as possible in order to co-ordinate and manage the establishment of the safe zone together".
"The safe zone shall become a peace corridor, and every effort shall be made so that displaced Syrians can return to their country," the embassy added.
On Saturday, Turkey's defence minister said the joint operations centre was operating at "full capacity", and that "the destruction of terrorist emplacements and fortifications" had begun.
The Kurdish-led Autonomous Administration of North and East Syria confirmed on Tuesday that the YPG had "removed some military fortifications" and "begun withdrawing a unit and heavy weapons" in the Ras al-Ain area over the weekend, and that similar steps were taken in Tal Abyad on Monday.
"These procedures were done to ensure our commitment to these understandings [with Turkey and the US] and to show how we are interested in a reaching a solution by way of a peaceful dialogue with neighbouring countries," it added.
The US military published photographs last week that it said showed SDF forces destroying fortifications. "This demonstrates SDF's commitment to support implementation of the security mechanism framework," it added.
The US has not specified the size of the "safe zone", but Turkey wants it to be 30-40km (19-25 miles) deep.
SDF spokesman Mustafa Bali told Reuters news agency on Tuesday that it would be only 5-14km (3-9 miles) deep and would include rural areas and military positions, not cities or towns.
The YPG and SDF would hand over control to military councils formed by local fighters in the area, which would be patrolled by Turkish and US forces based inside Turkey, Mr Bali said.
The Turkish military has twice sent troops into northern Syria to push YPG fighters away from its border since the Syrian civil war began. The last operation was in the western Afrin region in 2018.