"We don't understand the reason, in each case, why there should be a military popup airfield or something like that to start with," Ivanov told NBC television in an interview in Moscow on Thursday.
"If we think about terrorism, I understand, as a defence secretary, that the United States needs some transit points on the way for their troops to reach the area of what is now called the Big Middle East," he said.
Ivanov said he could imagine the need for such establishments, bases, in areas such as, for example, Bulgaria or Romania, but not in countries like Poland or the Baltic states.
"It's not the Cold War. The Cold War is dead. And we are not competing on an assumption that what is good for you is bad for your partner. We try to build our relations with the United States as a win-win situation," Ivanov said.
In Moscow late last month, US Secretary of State Colin Powell announced plans to establish a series of military bases in former Warsaw Pact countries.
"It's not the Cold War. The Cold War is dead"
defence secretary, Russia
But, in a bid to assuage Russian fears over Washington's intentions, Powell stressed that they would not be big bases and would be used for training or as staging areas for responding to "dangerous crisis places" in Central Asia, the Gulf and the Middle East.
On relations between Washington and Moscow, Ivanov said, "We have some contradictions, but strategically, we won't get back to the situation of the Cold War. Never. I believe that."
On Iraq, Ivanov said the US-Russian disagreement leading up to the war needs to be laid to rest.
"Here, there is no irony and no effort to gloat on the United States' failure to find such weapons of mass destruction," he said.