Barack Obama, the US president, said a day earlier that the decision to abandon the Bush administration's plans was taken after a change in Washington's perception of the threat posed by Iran.
Following a review, US intelligence decided short- and medium-range missiles from Iran now pose a greater near-term threat than the intercontinental ballistic missiles the Bush plan addressed.
A new missile-defence plan would rely on a network of sensors and interceptor missiles based at sea, on land and in the air as a bulwark against Iranian short- and medium-range missiles, said Robert Gates, the US defence secretary.
Vladimir Putin, Russia's prime minister, praised Obama's decision and urged the US to cancel Cold War-era restrictions on trade with Russia.
Putin described the move over the "defence shield" as a "correct and brave" decision.
In his speech, Rasmussen said long-range ballistic missile technology in the hands of such countries as North Korea and Iran threatened the West and Russia in large part because it could lead to regional proliferation.
"If North Korea stays nuclear, and if Iran becomes nuclear, some of their neighbours might feel compelled to follow their example," he said.
"The proliferation of ballistic missile technology is of concern not just to Nato nations, but to Russia too."
Rasmussen said Nato and Moscow had failed to jointly take on global security threats including terrorism.
"When the Cold War ended 20 years ago, Nato and Russia developed rather unrealistic expectations about each other," he said.
"Those flawed expectations ... continue to burden our relationship."
The secretary general did not elaborate on how, or to what extent, the Russian, Nato and US anti-missile systems could be linked up.
Russian leaders had threatened to deploy short-range missiles to the Baltic enclave of Kaliningrad near Poland if the US moved ahead with the missile defence plan in Europe.
On Friday, Russia's Interfax news agency quoted an unnamed Russian military-diplomatic source as saying that such retaliatory measures would now be frozen and, possibly, fully cancelled in response to Obama's decision.
In the past, Russia has said it is ready to jointly work on missile defence with Nato and the US, but it viewed Iran as being far from obtaining long-range missile technology and said it was necessary to jointly analyse missile threats from the country and other nations before taking any further action.
In 2007 Putin, Russia's president at the time, offered the use of a Soviet-era radar in Azerbaijan to the US as an alternative to the Bush administration's missile defence plan for Eastern Europe.
The then-US administration said the facility could not replace the planned missile shield.
Nato allies have engaged in technical work with the Russians on missile defence in the past, but it slowed down in recent years as the relationship became strained over Nato enlargement and Moscow's war with Georgia.
Turkey's military said on Friday that it was planning to spend $1bn on four long-range missile defence systems but denied it was buying missile interceptors for use against Iran.