Carter's order made it clear that the two nations have common ground when it comes to fighting Islamic State, and the goal should be to take the fight to Islamic State and not to defend the regime of Syrian President Bashar al-Assad.
"Another purpose of the talks will be to ensure Russian military activity in Syria does not interrupt operations by U.S.-led coalition forces against Islamic State," Cook said.
Details and timing of the conversations will be worked out in the coming days, Cook said.
The announcement comes after U.S. President Barack Obama's meeting with Russian President Vladimir Putin on Monday at the UN General Assembly in New York.
Putin on Sunday condemned U.S. support for rebel groups in Syria while defending his backing of al-Assad in the multi-sided civil war. The U.S. has described Russia's support for al-Assad as a mistake and insisted that he cannot be part of a diplomatic solution ending the war.