He went on to warn Western countries against taking part in the alliance in words that echoed those of the late founder of al-Qaida, Osama bin Laden.
"This is what will cause the battle to be transported to the hearts of your own homes; because Muslims will not stand idly by and watch Muslims be bombed and killed in their countries, while you are safe on your countries. The price of war will not be paid by your leaders alone. You will pay the biggest price," he said.
The recording appeared genuine and corresponded with Associated Press reporting.
The United States and five Arab allies launched an air campaign against Islamic State fighters in Syria on Tuesday with the aim of ultimately crushing the extremist group, which has created a proto-state spanning the Syria-Iraq border. The U.S. has been carrying out airstrikes against the group in neighboring Iraq since August.
Watch: An Explainer: Militant Groups in Syria
Some of the initial strikes targeted the Nusra Front, hitting several of its facilities and killing dozens of its fighters. Washington said it was trying to take out an al-Qaida cell known as the Khorasan Group that was actively plotting attacks against Americans and Western interests.
Syrian rebels have expressed anger at the coalition airstrikes, both because they have targeted the Nusra Front -- which they see as an ally -- and because they are not hitting pro-government forces, which are the best placed to benefit from any rolling back of the Islamic State group. The Nusra Front's ultimate goal is to impose Islamic law in Syria. But unlike the Islamic State group, it has fought alongside other rebel groups, seeing the overthrow of Assad as its first priority.
Al-Golani warned the airstrikes would weaken the rebels.
"Those of our men who were targeted in the shelling... the effect of their loss will be witnessed by the entire conflict, not just on the (Nusra) Front alone."
The Nusra Front leader also warned other rebel groups not to coordinate with the U.S.-led alliance. Washington has promised to arm and train more Syrian rebels to help fight the Islamic State group.
The al-Golani speech came hours after the group's spokesman warned that Muslims would attack countries taking part in the coalition air raids.
The Islamic State group -- an al-Qaida breakaway faction rejected by the global terror network -- controls a vast tract of land stretching from the Turkish border in northern Syria to the western outskirts of Baghdad, where it has declared a self-styled caliphate ruled by its brutal version of Islamic law. Its aggressive push across Iraq over the summer spurred the U.S. to form a coalition against the group.
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On Sunday, explosions lit the sky for two hours in the northern Syrian town of Tel Abyad as airstrikes, likely by the coalition, targeted a refinery operated by the militant group, said an eyewitness and activists.
"Our building was shaking and we saw fire, some 60 meters (65 yards) high, coming from the refinery," said Turkish businessman Mehmet Ozer, who lives in the nearby Turkish border town of Akcakale.
The Turkish news agency Dogan said the strikes targeted an oil refinery and the local headquarters of the Islamic State group. U.S. Central Command, which is overseeing the air campaign, did not immediately comment on the strikes.
The U.S.-led coalition has been targeting Islamic State-held oil installations across Syria, aiming to cripple the group's finances. The group is believed to earn some $3 million a day from selling smuggled oil on the black market as well as kidnapping and extortion.
The coalition includes Saudi Arabia, Bahrain, the United Arab Emirates, Qatar and Jordan. Several European countries also are contributing to U.S. efforts to strike the Islamic State group in Iraq, including France, the Netherlands, Denmark, Belgium and Britain.
The Britain-based Syrian Observatory for Human Rights says at least 19 civilians have been killed so far in coalition strikes in Syria. Most recently, six oil workers in the far northeast province of Hassakeh were killed overnight, said the Observatory, which obtains information from a network of activists on the ground.
Overall, some 190,000 people have been killed in Syria's three-year conflict, and nearly one-half of the country's pre-war population of 23 million people has been displaced.
- AP