In the 2010 New START treaty, Russia and the United States set lower numerical ceilings on the weapons tested in the exercise.
But Putin has made clear further cuts depend, among other things, on Washington assuaging his concerns about anti-missile defences it is deploying, including a European shield Russia says will make it more vulnerable.
Russian and American leaders say nuclear war between the Cold War rivals is now unthinkable.
But critics say Putin -- in power since 2000 and back as military commander-in-chief since his return to the Kremlin in May after four years as prime minister -- is exaggerating potential threats from the West to bolster support at home.