BEIRUT, Lebanon — Across insurgent-held Syria over the past week, images have proliferated of protesters burning American flags, calling President Obama “the enemy of God,” and declaring that the American-led airstrikes against the Islamic State extremist group are helping the government of President Bashar al-Assad.

“America became the arm of Bashar the terrorist,” read a sign held by a child in Kafr Daryan, in Idlib Province, in one of the dozens of protests that Syrians filmed and uploaded to the Internet.

Some of the protesters are Islamic State supporters carrying its black flag, though in Raqqa, the northeastern city long run by the group, those demonstrations have grown smaller and smaller as the attacks have proceeded, with many residents relieved to see the extremists on the run.

But the execution of the strikes has also been criticized, in interviews as well as online, by numerous Syrians bitterly opposed to the Islamic State. These insurgents and opposition activists have pleaded for years for the United States to strike the Syrian government forces that have been bombarding their towns and villages, and they initially welcomed the strikes on the Islamic State as a helpful second best.