Russian President Vladimir Putin has said a recent ballistic missile test was in answer to US plans to create a defence shield in Central Europe.
Mr Putin said Russia's actions were not aggressive
Mr Putin said it was a "response to maintain the strategic balance in the world", in what he called a "new round of the arms race".
But US Secretary of State Condoleezza Rice said she was perplexed by the row.
Russia seemed to think and act as if it were in "another era", she said, seemingly referring to the Cold War.
In a speech in the eastern German town of Potsdam, Ms Rice added that the US wanted to see a powerful and also democratic Russia.
"We want Russia to be strong, but strong in 21st century terms - not just with a strong center, but with strong, independent institutions," she said.
"Democratic institutions and an open society are not a source of weakness. Nor is freedom of speech and freedom of the press a nuisance."
Disagreements over human rights and democracy are one of several factors which have led to deteriorating relations between the two countries in recent weeks.
'Not the initiators'
Russia tested a new intercontinental ballistic missile, which can be armed with up to 10 warheads, on Tuesday.
"Our American partners have left the ABM (Anti-Ballistic Missile) Treaty," Mr Putin told a press conference.
"We have warned them then that we will come out with a response to maintain the strategic balance in the world."
Mr Putin defended Russia's actions, insisting they were not the "initiators of this new round of the arms race".
"(Our partners) are stuffing Eastern Europe with new weapons," he said.
"A new base in Bulgaria, another in Romania, a site in Poland, radar in the Czech Republic. What are we supposed to do? We cannot just observe all this."
He added: "These actions by Russia should not be feared, they are not aggressive, it's just an answer to rather tough and unjustified unilateral actions by partners."
Washington wants to deploy interceptor rockets in Poland and a radar base in the Czech Republic to counter what it describes as a potential threat from "rogue states" such as Iran and North Korea.
The US maintains its system is not directed at the Russians, but Moscow says its security is being threatened.
Russia's test launch took place at the Plesetsk cosmodrome in northern Russia on 29 May.
The missile, called RS-24, was designed to evade missile defence systems, the Russian defence ministry says.
The test missile successfully struck its target 5,500km (3,400 miles) away on the far eastern Kamchatka peninsula, the Russian Strategic Missile Forces said.