BEIRUT -- The U.S. is struggling to counter anger among the Syrian opposition, where many believe that the air campaign against extremists in the country is only helping President Bashar Assad and that Washington is coordinating with Damascus, despite American insistence it backs the rebel cause.

Since the U.S.-led campaign of air raids and missile strikes in Syria began last Tuesday, American officials - many of them Arabic-speaking -- have been making appearances on Arab TV stations, explaining U.S. goals. They have repeatedly denied any cooperation with the Syrian government and say Washington still seeks Assad's removal.

But the messaging seems to be making little headway. The anger among the opposition over the air campaign points to a central difficulty in the U.S. strategy: The main aim of the international coalition it has assembled is to defeat the Islamic State group -- which has taken over much of Syria and neighboring Iraq -- but in Syria it is Assad's government that is best placed to benefit from blows to the extremists.

Most Syrian rebel factions sharply oppose the Islamic State extremist group and have lost hundreds of fighters trying to prevent it from taking over territory. The Free Syrian Army, an umbrella group of relatively moderate rebel factions, has welcomed the air campaign.

But resentment is high among the opposition that, after ignoring their pleas for greater help against Assad for years, Washington finally took action only to counter radicals it sees as a danger to U.S. interests.

What particularly alarmed the Syrian opposition is that in the opening salvo of the assault, U.S. warplanes also hit positions of the Nusra Front, an al-Qaida affiliate that is also one of the strongest rebel factions battling Assad's troops. U.S. officials say the strikes aimed to take out an al-Qaida cell that was a threat to the United States or Europe -- but rebel factions saw an important ally being pounded by the Americans. Civilian deaths -- around a dozen according to activists -- have added to the anger.

In several opposition-held towns in the northern Syrian provinces of Aleppo and Idlib, protesters emerged from mosques after Friday prayers to denounce the strikes.

"The Nusra Front came to help us when the whole world abandoned us," read one banner carried in the town of Maaret al-Numan, according to videos and photos of the protests posted online by activists. "America is shelling civilians and left the killer of civilians," read a banner, referring to Assad, carried by a boy in the town of Maaret Musreen.

On Friday, the top U.S. military officer, Gen. Martin Dempsey, said the U.S. and its allies are taking every precaution to limit civilian casualties, but said some are inevitable.

Other banners at the protests denounced Arab nations participating in the U.S-led air campaign, calling them "enemies of the Syrian people, not friends." Saudi Arabia, the United Arab Emirates, Bahrain, Jordan and Qatar -- all backers of the rebels -- have carried out or given logistical support to the airstrikes. The video and photos were in line with AP reporting from the towns.

Reactions are complicated

"I was with the strikes and now I changed my mind," said one opposition activist from the central city of Homs who is currently in neighboring Turkey. "They are attacking civilians, leaving the regime alone and attacking the Nusra Front, who were fighting against Daesh," he said, using the Arabic acronym of the Islamic State group. The activist spoke on condition of anonymity for security reasons.

The suspicion runs deep among the opposition that Washington is coordinating with Assad's government despite repeated denials.

Damascus has been happy to present itself as working with the U.S. Hours after the strikes began, Syria's Foreign Ministry said in a statement that Damascus's envoy to the U.N. was informed about the attacks hours in advance. Assad voiced his support for "any international anti-terrorism effort" and said Syria is continuing to fight a war against "extremist terrorism in all its forms."

"Washington and its allies are in the same trench with the Syrian army in fighting terrorism," the pro-government newspaper Al-Watan proclaimed in a headline.

Ahmad al-Masalmeh, an opposition activist in the southern province of Daraa, said, "we keep hearing American officials saying that they refuse to coordinate with Assad and that he will not be a partner in the war against terrorism... In reality there is complete and full coordination."

Speaking to The Associated Press via Skype, al-Masalmeh said Assad's forces are not shooting at the warplanes and that government air raids cease whenever there are airstrikes by the U.S.-led coalition, hinting that they are informed in advance not to fly.

U.S. officials deny such claims.

"We never coordinated with the Syrian government and our stance toward the Syrian government did not change," State Department spokesman Ryan Gliha told Lebanon's leading LBC TV in fluent Arabic. He said Damascus was informed of the strikes through the U.N. channel but "we did not ask for permission."

Joshua Baker, another State Department spokesman fluent in Arabic, told the Dubai-based pan-Arab Al-Aan TV that the U.S. is coordinating with moderate Syrian opposition fighters known as the Free Syrian Army.

"These strikes will strengthen the moderate opposition," he said, underlining that the U.S. does not support Assad. "We believe that Assad lost his legitimacy."

The opposition, however, counters that striking Assad's troops - or the Shiite guerrillas from Lebanon's Hezbollah group that have been instrumental in backing them -- would be of greater help.

"There are lots of terrorist groups in Syria. It's not only Daesh," said Abu Omar, an activist based in the northern city of Aleppo, pointing to Hezbollah and Iraqi Shiite militiamen backing Assad. "Why aren't they attacking Hezbollah fighters?"

"When they bomb the Nusra Front they are doing (Assad's) regime a favor," said Abu Omar, speaking on condition he be identified by his activist nickname for security reasons. "Until now the main side benefiting from the strikes is the regime."