“The training now is under way and we’ll just have to see how that goes,” Mattis told reporters during his trip to Paris, France.
The Manbij patrols are part of a “road map” Turkey and the US agreed on in June to defuse tensions amid demands for the withdrawal of Washington-backed Kurdish militants from the flashpoint town.
Mattis said Washington was currently working with trainers, and that it would be followed by a few weeks of training with Turkish troops before the start of the joint patrols.
“We have every reason to believe the joint patrols will be coming on time, when the training syllabus is complete so that we do it right,” Mattis added.
The road map agreed in June called for the withdrawal of the so-called Syrian Democratic Forces (SDF), a Kurdish-dominated and anti-Damascus militant group that has the support of Washington, from Manbij.
Ankara considers the SDF as largely composed of militants from the People’s Protection Units (YPG), viewed by the Turkish government as a terror group and the Syrian branch of the outlawed Kurdistan Workers’ Party (PKK). The latter has been fighting for an autonomous region inside Turkey since 1984.
The Syrian government has given a degree of authority to the Kurdish regions to run their own affairs in the face of a foreign-backed militancy. The US, however, has used the vacuum to establish a foothold in those regions with the help of militants.
Washington angered Ankara by announcing a plan for the formation of a Kurdish militant force in Syria near the Turkish border, prompting Ankara in January to launch a cross-border military operation inside Syria, code-named Operation Olive Branch, with the aim of eliminating the YPG militants from northern Syria, particularly the Afrin region.
Turkish troops captured Afrin in March, and threatened to take the battle to nearby Manbij.
Ankara has repeatedly accused Washington of failing to fulfill its promise regarding the withdrawal of its allied militants from Manbij after the purge of the Daesh terrorist group in August 2016.
Earlier this year, President Recep Tayyip Erdogan threatened to push Turkey's Afrin offensive against the YPG militants eastward to Manbij, where US forces are stationed, risking a confrontation between the NATO allies.
Syria has strongly denounced the presence of Turkish and US troops around Manbij.