U.S. State Department spokesman Sean McCormack said Putin's comments were "not helpful, certainly surprising. They have more of the ring of 1977 than they do 2007."
NATO has also criticized Putin over his remarks.
During his one-day visit to Prague, Bush will also address a pro-democracy conference. In his speech, he is expected to talk about difficulties of promoting democracy in countries such as Russia.
Prague is the first stop on Bush's six-nation European tour which will include the Group of Eight (G8) major industrial nations' summit in Germany this week where he is set for a meeting with Putin.
(compiled from agency reports)