First Deputy Prime Minister Sergei Ivanov linked the possible move to US plans for a missile defence system in Poland and the Czech Republic.
Russia has already threatened to hit back by targeting missiles at Europe.
Mr Ivanov said there would be no need to move extra forces to Kaliningrad if the US agreed to use Russian facilities instead of the Polish and Czech bases.
Russia says the US plans for a limited missile defence shield, including bases close to Russia's borders, represent a threat to its security.
First deputy prime minister
US President George W Bush has described the idea as "innovative" but indicated that the US will press ahead with the plans for a radar station in the Czech Republic, and a missile base in Poland.
The US says its missile shield is not directed at Russia, but at what it considers "rogue states" such as Iran.
"If our proposals are accepted, the need will disappear for Russia to deploy new missile weaponry in the European part of the country, including in Kaliningrad Region," Mr Ivanov said, on a visit to Uzbekistan.
"After this, you will forget about the term 'Cold War'. It will simply disappear. There simply won't be cause for speaking of it," he added.
"If our proposals are not accepted - and I cannot rule that out... an asymmetrical and effective response has been found."
Mr Ivanov is a former defence minister, and his current brief includes overall control of the defence sector. He is also seen as a possible successor to President Putin.
Correspondents say Mr Ivanov's comments indicate that US hopes of toning down Russia's Cold War-style rhetoric by hosting a relaxed weekend meeting between President Vladimir Putin and Mr Bush in Maine have not borne fruit.