"Analogous actions by the Soviet Union, when it deployed missiles in Cuba, prompted the 'Caribbean crisis,' " Putin said at the conclusion of an European Union-Russian summit, using Russian terminology for the Cuban missile crisis.
"Such a threat is being set up on our borders," he said.
At the same time, Putin suggested the tension was much lower than during the Cuban missile crisis because Russian-U.S. relations have moved on since the Cold War. He said he feels the United States is listening to Moscow's concerns about its missile plans.
He said his relationship with President Bush, whom he called a friend, helps solve problems in ties with the U.S.
CBS News national security correspondent David Martin said he doesn't think Putin's talking about the threat of another nuclear confrontation.
"I think he's referring to the fact that after the Soviets were forced to back down, they embarked on a major buildup of nuclear arms that eventually brought them to parity with the U.S., which at the time of the missile crisis had vast nuclear superiority," Martin said.
Putin also said Friday that he would not assume presidential powers if he became prime minister after stepping down as Russian president.
"If someone thinks that I intend to move, let's say, into the government of the Russian Federation and transfer the fundamental powers there, that's not the case," he said. "There will be no infringement on the powers of the president of the Russian Federation, at least while it depends on me."
Putin suggested earlier this month that he could become prime minister after his second presidential term ends in May, leading some to speculate that the substantial powers now invested in the presidency might be transferred to the prime minister.
After repeating his insistence that he does not intend to change the constitution in order to run for a third consecutive term, Putin said Friday that he had not yet decided where and in what capacity he would work as former president. He is expected to remain an influential figure in Russia.
Russia holds parliamentary elections in December and a presidential vote three months later.