"This is not Rocky IV," he said, referring to the 1990 film depicting a battle between East and West, in which Rocky Balboa fights then-Soviet Union boxer Ivan Drago.
"Believe me. We don't see it that way", he added.
His comments come after Mr Putin ordered an urgent drill to test the combat readiness of its military forces amid tensions with the West over Ukraine.
According to the Defence Minister Sergei Shoigu, the manoeuvres commencing on Friday will last four days.
He added the exercise will involve ships of the Baltic and the Northern Fleets and the air force.
Shoigu's statement made no reference to Ukraine, where tensions remain high following the ousting of Russia-backed President Viktor Yanukovych.
Mr Kerry said he would "decline to speculate" on the whereabouts of Mr Yanukovych or whether he should be prosecuted for war crimes.
"We need to work together in what does not have to be a zero sum game to provide the capacity of the people of Ukraine to choose their future," Kerry said. "That's all that's at stake."
- The Independent