The Syrian Observatory for Human Rights citing unnamed sources said "the patrols of each party will move within its areas, without entering the other party’s areas."
US and Turkish diplomats endorsed a "road map" on Tuesday "to include taking steps to ensure the security and stability of Manbij."
The two NATO allies have been at odds over the US-led anti-ISIS coalition’s support for the Syrian Democratic Forces (SDF), composed largely of Kurdish Peoples’ Protection Units (YPG), which Ankara considers a terrorist organization.
The YPG announced on Wednesday it had withdrawn its military advisors from Manbij; however, a spokesperson later told Rudaw that "YPG artillery in Manbij belongs to Manbij Military Council."
However, the Observatory reported on Saturday that "no members or advisors have withdrawn from Manbij city until now."
Military and civil councils have been established in major population centers liberated by the SDF.
An explosion rocked the main square sending shrapnel into a 35-year-old civilian who was driving home, the Manbij Military Council reported on Sunday. The patient, Hassib Shaikho al-Omair, is stable and expected to be discharged, the council added.
Local forces deployed after a second bomb exploded near the Euphrates Hospital in Manbij, but the council reported no physical damage.
US Department of Defense spokesperson for Iraq and Syria Eric Pahon told Rudaw on Friday that the "bilateral roadmap" is a "huge step forward."
"This is great dialogue between the US and our NATO ally Turkey and we look forward to this increased cooperation," he said.
After meeting with US counterpart Mike Pompeo, Turkish FM Mevlut Cavusoglu expressed hope that the US will “stand with us” in regards to Ankara’s concern over the YPG.
“I am very glad that we have achieved a significant progress. I can say that it was a very fruitful and successful meeting,” he said, according to Turkey’s state-run Anadolu Agency.
The US maintains force presence and base in Manbij.
A delegation from the coalition visited the city's civil administrative center to assure the people of Manbij of its continued protection against external threats aimed at destabilizing security and stability, the MMC reported on Thursday.
The coalition delegation included US Maj. Gen. James B. Jarrard, a special operations commander, and veteran US diplomat Amb. William Roebuck. They met with the head of the MMC Mohammed Abu Adel.
"If the patrols are only on the front lines, we don't have a problem with that," said Abu Adel, according to Voice of America. "But not inside the town."
Ilham Ahmed, co-chair of the political wing of the SDF, said the US delegation gave guarantees that no Turkish or Turkey-backed Syrian forces will enter Manbij, according to VOA.
