A nightmare scenario could be that "one day -- and I literally mean one day -- he (Putin) just seizes Riga and Tallinn ... That would literally take him one day. There's no way they could resist," Brzezinski said.
"And then we'll say how horrible, how shocking, how outrageous. But, of course, we can't do anything about it," he said, without risking a potential nuclear conflict.
The US needed to impart to Russia that NATO forces would back their allies if it invaded any of the Baltics, he said.
"I think deterrence has to have meaning. It has to have teeth in it. And it has to create a situation in which someone planning an action like that has no choice but to anticipate what kind of resistance will lie in counter," he said.
"I do recommend pre-positioning of some forces," in those "tripwire" countries, he said, but in a way that was not provocative.
"An American company (of troops) in Estonia is not going to invade Russia," he added.
Putin would understand that, "but he will know that if he invades Estonia, he will encounter some American forces on the ground. And better still, some Germans, some French. And some Brits, of course," he said.