The Britain-based Syrian Observatory for Human Rights said the vast majority those killed, 746 people, were Islamic State militants, while another 68 were members of al-Qaida's Syrian affiliate known as the Nusra Front.
At least 50 civilians, including eight children and five women, also have been killed in the airstrikes, the group said.
The US-led coalition's aerial campaign in Syria began before dawn on September 23 in what President Barack Obama has called an effort to roll back and ultimately destroy the Islamic State group.
The militant extremist group has been the primary target of the coalition's strikes, although on at least two occasions the United States has targeted what it says is a specific cell within the Nusra Front allegedly plotting attacks against American interests.
The airstrikes in Syria expanded upon a US-led operation in neighboring Iraq against the Islamic State group, which has seized control of a large chunk of territory spanning the two countries.