Abu Mohammad al-Golani heads Jabhat al-Nusra, also known as Nusra Front, which has emerged as one of the most effective among rebel groups fighting Assad.
The Britain-based Syrian Observatory for Human Rights, which closely monitors the fighting in Syria, said senior Nusra Front leaders contacted by activists in Latakia and the eastern Deir el-Zour province denied al-Golani had been killed.
A rebel commander in a Damascus suburb contacted by The Associated Press said he believed al-Golani was "alive and well" based on his contacts with other fighters including those from Nusra Front. He declined to elaborate or be identified for security concerns.
The report comes as the fragmented rebels have suffered significant losses on the battlefield.
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Syrian troops killed at least 40 opposition fighters, including Nusra Front members, earlier yesterday in an ambush near Damascus, the government said.
State TV said al-Golani was killed in the coastal province of Latakia. It did not say when or give other details. News of his death was not mentioned in the main headlines of the TV's late night news bulletin.
Al-Golani, who fought previously in Iraq, is a shadowy figure who is believed to have spent time recently in rebellious suburbs south of Damascus. Rebels have also gained footholds in mountainous regions of Latakia, which is largely loyal to Assad, and he may have gone there to direct fighting.