BEIRUT—U.S.-backed Arab and Kurdish force buttressed defenses in the outlying neighborhoods of the Syrian city of Manbij after driving out Islamic State fighters and cutting one of its key supply routes, as residents took to the streets over the weekend to celebrate their freedom.

The Syrian Democratic Forces are preparing to defend the city against Islamic State counterattacks, Ahmad Hisso Araj, a spokesman for the force, said Sunday, two days after capturing Manbij. The extremist group’s most likely mode of attack, he added, would be suicide car bombs carried out in acts of desperation and revenge.

“Their spirits have been broken,” he said. “They can only target us from a distance.”

People were seen singing, dancing and playing loud music on the streets of Manbij, according to social-media posts and local reports, acts for which they would likely have faced harsh punishments under the Sunni extremist group’s rule. Some men were seen performing the “dabke”—a popular folk dance in some parts of the Arab world.

A few men were seen shaving their beards, while some women removed their veils. People were also seen smoking on the streets, another act that Islamic State banned and punished severely.