The missiles would be similar to those based in Alaska and California
Russian President Dmitry Medvedev has said that a preliminary deal allowing the US to site missiles in Poland is aimed against Russia.
Poland will host the missiles as part of a defence shield the US says it needs against "rogue states" like Iran.
But Mr Medvedev said it demonstrated that Russia's concerns about new systems in eastern Europe were valid.
"The deployment of new anti-missile forces has as its aim the Russian Federation," he said.
Mr Medvedev was speaking at a press conference after holding talks with German Chancellor Angela Merkel over the on-going unrest in Georgia.
Under the deal signed on Thursday, the US will install 10 interceptor missiles at a base on the Baltic coast in return for help strengthening Polish air defences.
A top general in Moscow said the move would worsen ties with the West already strained by the Georgian conflict.
Russia's envoy to Nato has meanwhile been quoted as saying the timing of the deal shows its true purpose is to counter Russia's "strategic potential".
At a press conference in Moscow on Friday, Russia's deputy chief of general staff, Gen Anatoly Nogovitsyn, said the US move "cannot go unpunished".
"It's a cause for regret that at a time when we are already in a difficult situation, the American side further exacerbates the situation in relations between the United States and Russia," Gen Nogovitsyn said.
The deployment of new anti-missile forces has as its aim the Russian Federation
Russia's envoy to Nato, Dmitry Rogozin, meanwhile reportedly criticised the decision to sign the deal during a "very difficult crisis in the relations between Russia and the United States over the situation in Georgia".
Mr Rogozin told Reuters news agency the timing showed "the missile defence system will be deployed not against Iran but against the strategic potential of Russia".
Moscow has long argued the project will upset the military balance in Europe and has warned it will be forced to redirect its missiles at Poland.
The US has urged Russia to withdraw troops that have fought with Georgian forces after Tbilisi attempted to retake the separatist region of South Ossetia late last week.
"I consider that the United States is not acting in a cautious manner in this situation," Mr Rogozin said, when asked about US-Russian relations and the situation in Georgia.
Polish Foreign Minister Radoslaw Sikorski told the BBC's World Tonight programme on Thursday that the timing of the missile deal had nothing to do with hostilities in Georgia.
"We agreed this negotiating phase a week ago, which was... before the events in Georgia, and because of the US calendar there was some urgency," he said.
"But, what is crucial, and what decided the success of the talks over the last couple of days, was that the US offered us new proposals."
Unlike the US, Poland sees Russia as a bigger threat to its security than so-called rogue states such as Iran, the BBC's Adam Easton in Warsaw says.
Russian Foreign Minister Sergei Lavrov is reported to have cancelled a scheduled visit to Poland shortly after the deal was announced.
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