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 to 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.
The way the strikes are being carried out has deepened suspicions that the United States has abandoned the goal of ousting Mr. Assad, according to several rebel commanders who have received financing from the United States, diplomats in touch with insurgents and activists, as well as dozens of residents of opposition-held areas inside Syria who were interviewed by telephone or electronic messaging.
And on Tuesday, Mr. Assad’s foreign minister, Walid al-Moallem, told The Associated Press that the government was “O.K.” with the attacks.
The Assad opponents said they were troubled by reports of civilian casualties, and by the targets the United States has struck, including several headquarters and commanders of the Nusra Front, an insurgent group not previously advertised as a target, deep inside territory it shared with other anti-Islamic State insurgents in Idlib Province. While the United States lists the Nusra Front, an affiliate of Al Qaeda, as a terrorist organization, it is considered a tactical ally by many Syrian rebels, including some of those the United States has deemed worthy of support.
There are also complaints about what has not been struck. In northern Aleppo Province, Islamic State militants have been carrying out a weeklong assault on a Kurdish area, where residents have pleaded for military aid.
Four American airstrikes have hit the Islamic State in the area, but Kurdish fighters say they need more help. On Tuesday, residents continued to flee into Turkey as the Islamic State bombarded the area’s main town, Kobani, or Ain al-Arab, and stray shells sailed across the Turkish border.
“We wouldn’t have had to leave if the Americans hit ISIS,” said Mustafa Sheikho, who fled Shukur, a village 43 miles south of the border, and walked to Turkey with his family without food, since they had no time to pack any.
Given the suspicions of antigovernment Syrians, American strikes should have focused strictly on the Islamic State, said Mohammed Ghanem, a Syrian opposition activist now working for the Syrian American Coalition, a group that has lobbied for American intervention against Mr. Assad.
“You rout ISIS, establish good will, create trust, and then, working with the opposition, you go after Nusra,” he said.
“We are troubled by the expansion of scope of the campaign,” he added. “Hitting deep inside rebel territory without prior coordination or discussion with armed opposition or civilian opposition is frankly causing considerable harm to the purpose of this mission.”
Diplomats, aid workers and others who have long followed the conflict say they are perplexed that the United States would veer to targets other than the widely despised Islamic State on the very first day of the campaign.
At the same time, the many protests in support of Nusra after the strikes have undercut American efforts to portray other insurgents as moderate. Anger over the attacks has also appeared to increase public support for the Islamic State.
“God, Syria and the Islamic State,” protesters chanted in western Aleppo Province on Friday, replacing a chant from earlier in the uprising, “God, Syria and freedom.”
American military officials say that the majority of the airstrikes have been carried out against the Islamic State in eastern Syria and that precautions have been taken to avoid hitting civilians or civilian infrastructure.
“Our assessment is that sentiments are mixed among local Syrians regarding airstrikes, with as many supporting airstrikes and hoping for their expansion as there are those potentially opposed,” said Col. Patrick Ryder, a spokesman for United States Central Command. He added that reports of grain silos being hit were false.
Part of the challenge is that with no United States action to thwart Syrian aircraft, airstrikes carried out by the government may be attributed by civilians to the Americans. A recent airstrike in Idlib Province hit a town that is home to American-backed insurgents and a water project financed by the United States Agency for International Development.
While the United States military said that attack was not carried out by the American-led coalition, many Syrians believe it was — or express anger that the Americans took no action to prevent it, even though they were operating nearby.
In Deir al-Zour, in eastern Syria, many residents had fled the provincial capital to smaller towns, only to flee again when American airstrikes hit Islamic State oil installations there.
In Raqqa, though, which has borne the brunt of the Islamic State’s brutal rule, residents say they are not afraid of the strikes.
“The United States’ warplanes and rockets are smarter than the regime’s ones, so they will not target us,” said Abu Muthana, 50, who runs a fast-food shop in the city’s downtown.
Shops in the city are operating, and streets are busy, despite a lack of electricity. Many Islamic State militants have gone underground, or left to join the fight against the Kurds in Kobani. The fighters say they will take the Kobani area and rename its main city, from Ain al-Arab — spring of the Arabs — to Ain al-Islam.