The Pentagon said Thursday it is "aware" of Russia's interest in opening military-to-military communications with the U.S., but Defense Secretary Ash Carter has not yet decided if he will call his Russian counterpart.

Pentagon press secretary Peter Cook said Carter "knows Russia well," but has so far decided that having any conversations with Russian military leaders wouldn't be beneficial to the U.S.

The Russian foreign defense minister told Secretary of State John Kerry that he would like to open military-to-military communications between the two countries.

"We're aware of the Russian interest conveyed in that conversation with Secretary Kerry, and Secretary Carter is consulting with his colleagues on the national security team as to exactly the best path forward," Cook said.

Russia has been flying military supplies and advisers to Syria to support the regime of President Bashar Assad. The U.S., which is trying to train moderate Syrians and conducting its own airstrikes in Syria, has called supporting Assad "counterproductive" and urged Russia to stop.

Russian President Vladimir Putin, however, said he will continue to deliver support to the Syrian government.

Russian and U.S. planes operating in the airspace over Syria and Iraq has raised questions about keeping aircraft from colliding, but the Pentagon has been adamant that there is no "deconflicting" to do right now.