Russian President Vladimir Putin has compared US plans for a missile shield in Europe to the Cuban missile crisis of the 1960s.
Mr Putin has pledged to boost Russia's defences
The crisis saw the US and Soviet Union go to the brink of nuclear war.
Mr Putin, at a summit with EU leaders in Portugal, said the situation was "technologically similar".
But he argued there would be no repeat because Russia and the US were "not enemies anymore... we are partners" and President Bush was a "personal friend".
The 1962 stand-off was triggered when US spy planes discovered Soviet missile bases in Cuba, within striking distance of the American mainland.
Moscow's decision to deploy these weapons in Cuba was at the time seen as a response to the build-up of powerful US missiles in Europe.
Tensions were only defused when Soviet leader Nikita Khrushchev agreed to dismantle the bases in return for guarantees that Washington would not attack communist Cuba.
US President George W Bush has said there is a "real and urgent" need for a missile shield in Europe as a defence against possible attack by Iran and countries in the Middle East.
His defence secretary suggested this week that the development of the bases in countries such as the Czech Republic and Poland could be slowed while Russian concerns were addressed.
The US and Russia are eager to develop new missile systems
President Putin said: "Let me recall how relations shaped up in a similar situation in the mid-1960s.
"Similar actions by the Soviet Union, when it deployed missiles in Cuba, provoked the Caribbean crisis. For us, technologically, the situation is very similar."
But he said the current tensions would not reach the pitch attained during the Cuban crisis.
"I agree completely with President Bush when he says that Russia and the US are not enemies anymore... we are partners. I am fully justified in saying that just as he calls me a friend, I can call him a personal friend too."
Mr Putin said Russia had put forward proposals in the area of security but "we have unfortunately not yet received any answers".
US state department spokesman Sean McCormack said there were "clear historical differences" with the Cuban crisis.
"I don't think that they are historically analogous in any way, shape or form."
EU leaders at the Portugal summit were hoping to speed progress towards a long-term agreement with Russia, that would extend to sensitive areas such as energy supplies.
The EU has been hoping to smooth strained relations with Russia
The EU depends on Russia for a third of its energy needs and has seen gas supplies disrupted for two successive winters.
European Commission President Jose Manuel Barroso confirmed a deal had been reached on sharing information on energy supplies to pre-empt sudden shortages.
"We have agreed today on a specific early warning mechanism to deal with problems in supply before they become a possible crisis," he said.
An agreement was also reached in Portugal on working together to curb the trafficking and consumption of illicit drugs and on raising the quota for Russian steel exports to the EU.
Disagreements with Russia over human rights and foreign policy overshadowed the start of the summit, with Russia's envoy to the EU warning that Moscow didn't "want to listen to any lectures".
In separate appeals, both Human Rights Watch and Amnesty International have urged EU leaders to speak firmly and with one voice about what the groups call the Kremlin's worsening human rights record.
The Kremlin also opposes the stance pursued by several EU members on Kosovo and Iran.
Russia opposes independence for the Serbian province of Kosovo and has also criticised recent moves to impose sanctions on Iran.