The US and Russian military will hold talks "as soon as possible" to avoid clashing in Syria, the countries' top diplomats say.
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Mr Putin spoke after meeting Barack Obama on the sidelines of the UN General Assembly (UNGA).
France has carried out its first air strikes against Islamic State militants in Syria.
Russian President Vladimir Putin has called for a regional "co-ordinating structure" against Islamic State (IS).
Syrian rebels have seized control of a key airbase in the north-western province of Idlib after a two-year siege.