The groups said in a statement that the announcement by the rejectionists of a caliphate is null and void, legally and logically.
Among the signatories were the Islamic Front, Syria's biggest rebel coalition, and Majlis Shura Mujahideen al-Sharqiya, an alliance in the eastern province of Deir Ezzor near Iraq, that includes the Al-Qaeda affiliate Al-Nusra Front.
The statement, signed by the religious bodies of each rebel group, went on to say that the Islamic State's announcement "changes nothing in terms of how we perceive them, or how we will deal with them".