BAGHDAD — The Islamic State deployed snipers on rooftops in Fallujah on Saturday in an attempt to quell an insurrection by Sunni tribesmen, Iraqi officials said, a flare-up that appears to indicate the group’s weakening grip on the city.

Small clashes took place in the Nazzal and Askali neighborhoods, said Sheikh Majeed al-Juraisi, a tribal leader from Fallujah who claims to be in contact with gunmen inside. Eissa al-Issawi, Fallujah’s mayor in exile, also confirmed the fighting – but with phone lines cut the reports were difficult to independently verify.

The fighting in the city about 45 miles west of Baghdad in Anbar province is a small but rare show of force against the Islamic State, which has controlled Fallujah for more than two years. The group’s hold on Anbar has been weakened, however, with Iraqi forces retaking the provincial capital of Ramadi, leaving Fallujah isolated and besieged.

With essential food and medical supplies scarce, frustration has been building in the city.

“If Daesh were the same strength that they were six months ago, they would have controlled the situation within hours,” Juraisi said, using an Arabic acronym for Islamic State. The group has been weakened in the city since it lost Ramadi, he said.

The sporadic fighting began Thursday when Islamic State members publicly insulted and humiliated an elderly man, according to Juraisi and Rageh Barakat, a member of the provincial council.