WASHINGTON — The United States has increased its forces near the northern Syrian town of Manbij as concerns have grown that fighting could erupt among the complex array of militias and Syrian and Turkish troops who are operating on the crowded battlefield near there.

Photographs of American troops in Stryker vehicles and armored Humvees flying American flags circulated on Saturday on social media. The American-led command that is fighting the Islamic State, a militant group also known as ISIS or ISIL, acknowledged the buildup around the town, but did not provide details.

“The coalition has increased its force presence in and around Manbij to deter any hostile action against the city and its civilians, to enhance local governance and to ensure there is no persistent Y.P.G. presence,” an American military spokesman said, using the acronym for the People’s Protection Units, Kurdish militia groups that have been trained by United States military advisers.

The Turks have repeatedly complained that the Y.P.G., which played a critical role in taking Manbij, has yet to vacate the city, despite American assurances that it has done so.