The US says the aim of the operation is to defeat DAESH and return Manbij to Syrian Arabs and the US-backed PYD forces will move back to east of Euphrates River.
The Pentagon on Monday said it's committed to conducting operations in Manbij which are consistent with commitments made between the US and Turkey.
"We have been clear with all elements of this operation that the aim is to defeat DAESH in Manbij and return it to the control and governance of the local population," Pentagon spokesman Adrian Rankine-Galloway told Anadolu Agency.
Galloway said the US is grateful for Turkey's partnership in the fight against DAESH and the aim of the ongoing operations by the US-led Syrian Arab Coalition (SAC) is to defeat the militant group and return Manbij to Syrian Arabs.
The statement by the Pentagon came hours after Turkish Foreign Minister Mevlüt Çavuşoğlu reminded the US commitment that the city will be left to its people after being liberated.
Defence Secretary Ashton Carter congratulated Manbij residents and the SAC for the "significant milestone" in successfully liberating Manbij.
Carter said he appreciated the Turkish government's support for the operation.
"The success in Manbij city will also help reinforce the growing isolation of Raqqa and enable us to achieve the next objective of our campaign in Syria - collapsing ISIL's [DAESH] control over that city."
Manbij is historically an Arab city and the main group fighting DAESH in the city is the SAC.
The PYD, a group Ankara does not recognise as a legitimate Syrian opposition, is fighting alongside the SAC.
Since operations began in May to liberate Manbij, the US has promised Turkey the PYD would leave the area after the city's liberation.
Manbij lies west of the Euphrates River.
Turkey wants the PYD to return to east of the Euphrates after Manbij's liberation as the city serves as DAESH's communications hub between the Turkish border and Raqqa, the self-declared capital of the militants.
Asked what the recent efforts were in the city's liberation from DAESH, the Pentagon said the situation was "very fluid" but US partners on the ground were "closing in" of the fight.
"The final positioning of forces is under the command and control of SAC and SDF [Syrian Democratic Forces].
We won't speculate as to a timeline," Rankine-Galloway said.