Medvedev says the deployment of an anti-missile system close to Russian borders "will of course create additional tensions."
"We will have to react somehow, to react, of course, in a military way," Medvedev was quoted as saying Tuesday by the RIA-Novosti news agency.
Russian officials have already warned of a military response to the U.S. plans, but the statement by the Russian leader was likely to further aggravate already tense relations with the West.
The United States says the missile-defense elements in Poland and the Czech Republic are aimed at blocking attacks by rogue nations such as Iran. Russia is convinced the shield is aimed against it.
Medvedev's comments come after he recognized two Georgian regions as independent nations, prompting criticism from the U.S. and Europe.
The White House sought to emphasize that Russia's conflict was with the world, not just with the United States. Several foreign leaders criticized Russia's action on the two provinces.
"Russia is making, I would say, a number of irrational decisions," said White House spokesman Tony Fratto.
"We hope that they hear the loud voices from the international community and understand that it's not in their long-term interests to take these kinds of actions," he said.
Vice President Dick Cheney leaves next week on a trip that includes a stop in Georgia; Fratto said no U.S. officials plan to go to Russia to appeal directly to leaders there.
Bush said the U.S. condemns Russia's actions; just a day earlier, he had appealed to Medvedev to refrain from recognizing the two provinces as independent, to no avail.
Barack Obama, who will become the Democratic presidential nominee this week, condemned Russia's move and said the U.S. should convene a Security Council meeting to do the same. He did not say how the Council would do that, given Russia's status as a permanent member.
Republican John McCain's wife was in Georgia, visiting refugee centers filled with ethnic Georgians who fled villages and neighborhoods in South Ossetia.
"The only place these people want to be is home, and they can't go home because of what has happened to them and because of the situation that the Russians have caused," Cindy McCain said in brief remarks Tuesday outside one of the centers in Tbilisi.
John McCain has been a strong critic of Russia and has proposed expelling Russia from the Group of Eight club of the world's major developed democracies.
In Washington, State Department spokesman Robert Wood said the U.S. is looking at a variety of options to respond.
"We're not trying to escalate anything," Wood said when asked whether disagreement between the West and Russia would jeopardize international cooperation. But, he added, "We obviously can't allow what Russia's done to go without there being some consequences."
He would not provide details about possible punishment the United States is considering.
Meanwhile, the United States dispatched a military ship bearing aid to a Georgian port city still patrolled by Russian troops.