Backed by air strikes by a US-led coalition, the SDF militia has trapped Daesh militants in a section of Baghouz village, near the Iraqi border.
Turkey has vowed to carry out a counterterrorist operation in Syria, east of the Euphrates, following two similar successful operations since 2016.
Current and former officials told The Wall Street Journal progress between US and Turkey on the Manbij deal is slow and therefore the military withdrawal is proceeding faster than the political track.
The attack, claimed by Daesh, comes as the Trump administration is planning to withdraw troops from Syria as the US president says Daesh has been defeated there. Turkey says it believes the assault will not change the US pull-out plan.
Regime leader Bashar al Assad's forces claimed to have entered the northern city after the YPG terror group asked for regime's presence. But sources from Manbij told TRT World the regime forces have not entered the city.
Turkey and the US have been carrying out joint patrols in Manbij as part of a deal that should see the withdrawal of YPG militants from the city to stabilise the Syrian region.
In a statement, the Elbubanna tribe said "We as the biggest tribe in Manbij support the patrolling of Turkish troops, which will play a major role in ensuring stability and security."
If the Manbij model is successfully implemented, eastern Syria could eventually become a joint US-Turkish zone of influence.
The YPG will be forced out of Syria’s Manbij in a few months, according to a roadmap drawn by Turkey and the US early this week. But Ankara is cautious over the deal's implementation as Washington has repeatedly delayed a withdrawal since 2016.
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