BEIRUT, Lebanon — American and Syrian warplanes screamed over the Syrian city of Raqqa in separate raids this week, ostensibly against the same target, the Islamic State militants in control there.

In the first raid, on Sunday, United States warplanes hit an Islamic State building, with no report of civilian casualties. On Tuesday, Syrian jets struck 10 times, killing scores of civilians, according to residents and Islamic State videos.

The back-to-back strikes, coming just days after President Bashar al-Assad of Syria declared that the West needed to side with him in “real and sincere” cooperation to defeat the extremist group, infuriated Syrians who oppose both Mr. Assad and the Islamic State. They see American jets sharing the skies with the Syrians but doing nothing to stop them from indiscriminately bombing rebellious neighborhoods. They conclude, increasingly, that the Obama administration is siding with Mr. Assad, that by training United States firepower solely on the Islamic State it is aiding a president whose ouster is still, at least officially, an American goal.

Their dismay reflects a broader sense on all sides that President Obama’s policies on Syria and the Islamic State remain contradictory, and the longer the fight goes on without the policies being resolved, the more damage is being done to America’s standing in the region.