The United States on Wednesday insisted it was not cooperating with Russia over Moscow's air strikes in Syria with Defence Secretary Ashton Carter describing them as "a fundamental mistake".

"I have said before that we believed that Russia has the wrong strategy –- they continue to hit targets that are not ISIL. We believe this is a fundamental mistake," Carter told a press conference in Rome, referring to the Islamic State group by an alternative name.

"Despite what the Russians say we have not agreed to cooperate with Russia so long as they continue to pursue a mistaken strategy and hit these targets."