WASHINGTON -- The United States and its allies should deploy troops to Baltic states to deter Russia from staging a possible incursion in those countries, former presidential national security adviser, Zbigniew Brzezinski, told lawmakers Wednesday.

The foreign policy expert, who served under president Jimmy Carter, told the Senate Armed Services Committee that he feared Russian President Vladimir Putin might try to take control over Baltic countries in a lightning move that could take NATO by surprise.

A nightmare scenario could be that "one day -- and I literally mean one day -- he 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 United States needed to make clear to Russia that it would US forces if it tried to invade 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 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 said.

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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.

Brzezinski also said that Western governments should provide "defensive" weapons to Ukraine to make Moscow's intervention more costly, while also sending a signal Ukraine would not be given membership in the NATO alliance.

His comments came as NATO chief Jens Stoltenberg said Russia had increased the amount of heavy arms it was sending into Ukraine while Kiev accused Moscow of deploying 9,000 troops inside its country.

The United States has sent troops to the Baltics, Poland and other eastern allies for high-profile exercises to reassure anxious government's over Russia's intervention in Ukraine. But US officials so far have not proposed stationing additional American troops permanently in the Baltics.