The Kremlin said Friday that 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 Friday that 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 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."

On the second and final day of his visit to Moscow on Friday, Kerry is meeting his Russian counterpart Sergei Lavrov to discuss ways to resolve the bloody five-year-long conflict.

Kerry's spokesman said that he would "explore initiatives in more detail" with Lavrov following a Thursday meeting with Putin, which Kerry said had been "serious and frank".

This diplomatic push comes as ferocious bloodshed in Syria persists following a series of failed ceasefires, and Russia and the United States appear increasingly at odds over the way forward amid heightened diplomatic tensions.

Speaking to NBC News in Damascus, in an interview broadcast Thursday, Assad insisted Putin and Lavrov had never raised the issue of his departure or a political transition.

"Russia's position regarding Assad's fate is well-known and has not undergone any kind of change," Peskov said Friday.