President Vladimir Putin and US Secretary of State John Kerry did not discuss direct military cooperation in Syria during talks aimed at reviving the stalled peace process in the war-torn country, the Kremlin said on Friday.

"The topic of direct military cooperation in the fight against terrorism did not figure" in the talks, Kremlin spokesman Dmitry Peskov told reporters after a leaked document revealed Washington was set to offer Moscow closer military cooperation against jihadist groups in Syria.

"An exchange of information is occurring but, unfortunately we have not begun real cooperation to significantly improve the effectiveness of efforts in the fight against terrorism."